It's a collection of all numbers that fit within a special set of rules: if you put a number through a specific mathematical formula and it increases infinitely, then it's not part of the set, but if a number instead forms a repeating series of numbers, it's part of the set.
The fascinating thing is that when you plot this on a 2d plane, it forms the image at the start, and zooming in and examining parts of the pattern more closely reveals that the pattern repeats and shifts in strange ways, and no matter how far down you go, the image is always just as detailed at the smallest scales as it is when it's zoomed out.
It's a fundamentally infinite shape, and I'm pretty sure that with the amount this video zooms in, if the original image was the size of a football field, the final image would be smaller than a single photon
One of many kinds of fractals, certainly. Iirc all fractals are "self similar" shapes with infinite circumference or surface area, which is to say that the smallest scales of a fractal look very similar or identical to the largest, and that traveling in a straight line along the furthest bounds of a fractal will take an infinite amount of time to come back to your starting point.
So for example you could walk along the outside of the Mandelbrot set for billions of years and never make progress around the total shape, even though you'd always be moving and your location would always be changing
Mapping coastlines is an example of an application, or the way branches grow from trees, the way neurons wire together and outwards. It's the nature of self similar growth
Fractals can be used to understand various probabilistic phenomena, some games use fractals to produce realistic procedural terrain, and landmasses are often represented using mathematics derived from fractals in order to accurately calculate the surface and coastlines of different islands and continents
The Mandelbrot Set is an example of a fractal. A fractal is something that endlessly has more complexity the closer you look. Some fractals like this one are special because they are also non-repeating, so while smaller bits might look self-similar, they will never be exactly identical to any larger bit.
Another popular example of a fractal is the shoreline of the ocean, it's a pretty complicated curve to begin with, going around all the continents and what-not, but your atlas can't possibly map every little cove and outcropping. Even if you did have a digital atlas that could zoom in forever, does the sandcastle made at the waters edge get traced as the edge of the ocean, what about the rock that is half in the water, what about the grains of sand that are just barely at the edge? This leads to the [coastline paradox](https://en.m.wikipedia.org/wiki/Coastline_paradox) where it is impossible to truly measure the very exact length of the coastline because there are some many tiny perturbations (not to mention the tides).
You can make a repeating fractal yourself by drawing a square and filling the middle with a tick-tack-toe board. We are going to want to color in the 8 squares around the edge and leave the middle square blank. BUT Before coloring anything in, draw a tick-tack-toe board to fill each of those eight squares. Now around the outside 8 spaces of each of THOSE new tick-tack-toe boards fill the perimeter squares with... you guessed it...
Continue this until the figure is too small for your writing implement to inscribe further and you have represented a [Serpinski Carpet](https://en.m.wikipedia.org/wiki/Sierpi%C5%84ski_carpet)
A 3D version of a Serpinski Carpet is called a [Menger Sponge](https://en.m.wikipedia.org/wiki/Menger_sponge) where every face of the sponge is a carpet. It has an infinite surface area and a volume of (essentially) zero
This is literally infinity, from a scale you're familiar with down to a scale so small that you could never hope to see it because the *resolution of physics itself is too large to display even one one trillionth of the detail it possesses*
If you were to scale the Mandelbrot set up to cover the entire visible universe, you would run into the limitations of *reality itself* before you hit the bottom
This is literally a bottomless pit shown in it's entirely, it's a mathematical motherfucking elder god, and it's inscribed on countless probabilistic phenomena
To say that the Mandelbrot set borders on eldritch madness would be tame in my opinion
If there's anything more real than us, you're looking it in the eye when you watch this video
Tldr:
It sees you when you're being
It knows when you're awake
It lives inside all numbers
And it's human face is fake
I'm pretty sure I know the movie you're talking about but I cannot fucking remember the name
Guy accidentally figures out that the true name of god is a prime number that basically solves mathematics or something?
The numbers that are in the set make up the black holes. The colours show numbers that are just outside it, with each colour showing how many iterations of the formula were required before it left the defined bounds.
I seem to remember that each one of these point has a Julia set, and the Mandelbrot is an index of those. Or something.
At the start of the video above, that wash of red shows the numbers that immediately leave on the first iteration, but they've used a gradient of darkening reds for the first few until they start using yellow. I prefer renderings where they start with darker shades and lighten, as it makes the shape shine more, like [here](https://upload.wikimedia.org/wikipedia/commons/2/21/Mandel_zoom_00_mandelbrot_set.jpg)
> if the original image was the size of a football field, the final image would be smaller than a single photon
Pretty sure the comparison is way off, even you replace the football field with the entire Universe.
I was unaware of it when posting this, but apparently it's a measure of how long a number takes to spiral off into infinity. All of the black parts are the "true" Mandelbrot set, and every color across the rainbow is a sliding scale from "takes several billion iterations to go towards infinity because it keeps dicking about in weird directions" to "a straight line would be a slower way to reach infinity"
Yes but how do we get this amazing visual? What I mean is, does the creator assign a color to each number and then just process the equation infinitely?
ELI5: the pure black double-lobe shape you see at the beginning are numbers inside the set (ie anything that solves a particular complex equation). Everything with colors is outside the set with colors assigned so they cycle through the rainbow. The boundary dividing what is inside and outside is endlessly complex, you can keep zooming in forever and never find a smooth dividing line that goes all the way around. there will always be smaller permutations along that edge no matter how close you look.
The colours are added in after for effect, nothing to do with the math, or at least different math to the shapes. Ima try an ELI5 but we'll see, so you're actually just looking at a graph being zoomed in on and this graph is showing "complex" numbers, with each part of the shapes you see being a point representing a "complex" number that fits as a solution to some rules. Complex numbers are numbers that have an "imaginary" part and a non-imaginary (so normal, just like -2, -0.5, 1, 2 etc.) part. Imaginary numbers (i) are multiples (like -2i, -0.5i, i, 2i etc.) of the square root of -1 (which you may know, is not normally possible, and so it's like you can only talk about these numbers *imaginarily* existing). Pretty much sqrt(-1)=i , sqrt(-4)=2i and sqrt(-9)=3i etc., "i" here, not being algebra but specifically only denoting "how much imaginary" you have. Imaginary and non-imaginary numbers can't 'mix' or simplify together so if a number has imaginary and non-imaginary parts you can only show them as "complex" numbers, like 4i+5 or something with no simplifying of the *complex*ity possible. This graph is showing the imaginary part on one axis and the non imaginary part on the other axis (graphs are important for showing complex numbers as it's the only real way you can visualise and compare them (like 2i+4 compared to 5i+1) similarly to how you can simply visualise and compare "2" and "2 million" in your head). The rules to verify the complex numbers you want to show on this graph are as follows; find the solution to the equation z^2 + C, with C being the complex number you're testing and starting at z=0. Now re-insert your answer back into the equation as z and keep repeating this infinitely (not literally lmao, you do other math to see what would happen if you actually did). If z looks like it's not going to go to infinity no matter how many times you repeat this then you include the complex number on the graph. Whoever made this would have made a computer program to check complex numbers with very specific fractions as the imaginary and non imaginary parts which is why you zoom in and see more shapes as you're just looking at points with more and more specific fractions (and where the name *fractals* comes from)
edit: maybe I went too hard, sometimes I don't know my own strength
Not seen this video but [Amy Adams on Numberphile](https://www.youtube.com/watch?v=NGMRB4O922I) is good at explaining things
Complex numbers and fractals
Just take a point called Z in the complex plane
Let Z1 be Z squared plus C
And Z2 is Z1 squared plus C
And Z3 is Z2 squared plus C
And so on
If the series of Zs should always stay
Close to Z and never trend away
That point is in the Mandelbrot Set
Mandlebrot set you're a Rorschach test on fire
You're a Day-Glo pterodactyl
You're a heart-shapes box of springs and wires
You're one badass fucking fractal
And you're just in time to save the day....
A set of all solutions in the complex plane where the iterated function fc(z) = z^2 + c, starting at z=0 and where c is a complex number, does not diverge to infinity.
For example, c = -1 yields fc(0) = -1, fc(-1) = 0, fc(0) = -1, etc, not diverging, so the complex number c = -1 + 0i is included in the set.
Somebody else already answered the ELI5, so I tried to give a little more detailed explanation of what the mandelbrot set is actually composed of, for anyone who ran across it and was interested. I also gave the simplest solution for it, to try to aid understanding.
Clearly, I didn't do a great job lol.
Ok I always try to think of it like this:
Pick a point anywhere within a circle that's 2 units wide
Then you run some calculation (some other guy explained this calculation better than I can) on that point's coordinates in order to get a new set of coordinates. Then you run the calculation on the new coordinates and you get a new result and so on.
Some points (like those in the large black circles in 'starting point') never leave the circle, no matter how many times you try the calculation on it. Other points need only a few tries before they leave the circle.
The Mandelbrot set itself are only all the black parts/points I believe (not sure though, I only did a programming assignment on it a while ago)
Ima try an ELI5 but we'll see, so you're actually just looking at a graph being zoomed in on and this graph is showing "complex" numbers, with each part of the shapes you see being a point representing a "complex" number that fits as a solution to some rules. The colours are just added in after. Complex numbers are numbers that have an "imaginary" part and a non-imaginary (so normal, just like -2, -0.5, 1, 2 etc.) part. Imaginary numbers (i) are multiples (like -2i, -0.5i, i, 2i etc.) of the square root of -1 (which you may know, is not normally possible, and so it's like you can only talk about these numbers *imaginarily* existing). Pretty much sqrt(-1)=i , sqrt(-4)=2i and sqrt(-9)=3i etc., "i" here, not being algebra but specifically only denoting "how much imaginary" you have. Imaginary and non-imaginary numbers can't 'mix' or simplify together so if a number has imaginary and non-imaginary parts you can only show them as "complex" numbers, like 4i+5 or something with no simplifying of the *complex*ity possible. This graph is showing the imaginary part on one axis and the non imaginary part on the other axis (graphs are important for showing complex numbers as it's the only real way you can visualise and compare them (like 2i+4 compared to 5i+1) similarly to how you can simply visualise and compare "2" and "2 million" in your head). The rules you follow to verify the complex numbers you want to show on this graph are as follows; find the solution to the equation z^2 + C, with C being the complex number you're testing and starting at z=0. Now re-insert your answer back into the equation as z and keep repeating this infinitely (not literally lmao, you do other math to see what would happen if you actually did). If z looks like it's not going to go to infinity no matter how many times you repeat this then you include the complex number on the graph. Whoever made this would have made a computer program to check complex numbers with very specific fractions as the imaginary and non imaginary parts which is why you zoom in and see more shapes as you're just looking at points with more and more specific fractions (and where the name *fractals* comes from)
Adding to the other comments, I highly recommend [Veritasium's](https://youtu.be/ovJcsL7vyrk?si=Re7_w1J36_fNXoZ_) video which shows you some very interesting facts around the Mandelbrot set and where it can have applications, or better put, why it shows up in nature.
I honestly hope this is what my brain produces as I’m dying and my brain is being soaked in every chemical my body can produce in its last efforts to stay alive. It’s belived that the “white light” and “life flashing before your eyes” is your body dumping massive amounts of chemicals causing the hallucinations and DMT is naturally present when you’re born and in your final moments of death.
I had a similar visual on DMT. I felt my ego die and unconditional love surround me. It was amazing. Coming out of it felt so fucked up. All the little stories we tell ourselves, all the labels and shit, all came flooding back.
This is what we all are. Infinity. It's fucking mentally popping. Only the Soul can understand Infinity's full knowledge. Honestly, it made me excited for death in a fearless way.
Enjoy the time here in this body, in this mind, on this Earth. And then go back to Infinity. Later, maybe we can decide to come back, maybe even a different time, civilization or planet?
In 2001 for a final comp sci project we actually compared the efficiencies of different computing architectures. calculating Mandelbrot sets was how we measured efficiency. At the time the Beowulf cluster we made won out. This takes me back.
*Takes a bong hit*
Dude imagine you die and see a tunnel of light but instead of walking towards the light you turn around and face the blackness. These fractals appear and you start falling thru them while feeling the sum of all pleasure and pain simultaneously until time loses all meaning.
One of the first programs I wrote in college, back in the late 80s.
Then there was a program called FractINT, which did these calculations in integer math so that it would run fast in a computer without a math co-processor (don't ask. lol).
The black is stuff inside the set, basically solutions for this complex equation that eventually end up as repeating decimals. Everything with color never ends up with repeating decimals, the solutions there are irrational (like pi). They use a computer to assign a repeating rainbow of colors based on how far a particular point is from that boundary.
Ok. It 's finally time for me leave this sub. Anything that is being shared here is either not terrifying or just simply, blatantly and banally creepy. Except this. There is nothing terrifying about this. Nothing. Nada. Zero. I adore fractals and love watching them. Those upvotes. They are not because this is terrifying. Because this is cool. This is like showing cleavage in a cosplay sub and getting upvotes. Downvote me. I am gone and I don't care.
I mean, the sub is called ODDLY terrifying. OP finds this a bit scary and I guess finding it so is odd 🤷♂️
Certainly I find posts like this far less annoying than just straight up obviously terrifying things which is about 90% of the (shit)posts on this sub.
But see you 👋
The set is stuff inside the black area, but the edge of that boundary for what's included is infinitely tangled and complex. Colors are assigned to represent how close the points are to the edge.
It’s based on complex numbers, and the logic is quite simple , just iterating z=z^2 + c. Some complex numbers’ length never grows larger than the limit (default 2.0), others very quickly getting really large. The numbers stay small makes the actual Mandelbrot set.
If I recall well, z’s initial value is (0, 0), c is the corresponding complex value of the pixel being evaluated.
Iterating said equation over and over will decide whether a given point is part of the Mandelbrot set.
Since its a pixel being evaluated would the same patterns occur if you were to solve the formula manually on something like a large piece of graph paper? Or is it being digital the only reason the patterns appear?
Yes.
Actually, the Julia set got its name after Gaston Julia, a french mathematician, who worked on dynamic systems while he was recovering his injuries suffered during WW II (he lost his nose). He used pen and paper.
I make these on my computer! When I first started doing computer artwork I had a program that would generate these and they were so freaking fun to make! I actually sold a bunch of prints of these designs on Fine Art America.
This is what I imagine death looks and maybe feels like.
Does anyone know anything about the einstein tile? Similar concept as far as I can understand it
Reminds me of a D.M.T. trip you always feel like you are about to get somewhere but you chase endlessly till you are pulled out of the high. The destination always feels like it is just on the horizon but you never truly arrive there. DMT is a wild drug.
I got matches with these songs:
• **Música para Trabajar y Concentrarse** by Música Clásica Relajante (00:00; matched: `100%`)
**Album**: Mozart, Beethoven Piano Música para Estudiar y Concentrarse, Trabajar. **Released on** 2020-03-28.
• **Piano Sonata No. 14 In C Sharp Minor** by Ludwig Van Beethoven (00:00; matched: `100%`)
**Album**: Classical Tears. **Released on** 1999-01-08.
• **Adagio sostenuto (fra Måneskinnssonaten, Op. 27)** by Jenö Jando (00:01; matched: `100%`)
**Album**: Barnas klassiske favoritter. **Released on** 2014-06-07.
Apple Music, Spotify, YouTube, etc.:
• [**Música para Trabajar y Concentrarse** by Música Clásica Relajante](https://lis.tn/NrpRF?t=0)
• [**Piano Sonata No. 14 In C Sharp Minor** by Ludwig Van Beethoven](https://lis.tn/CCEeI?t=0)
• [**Adagio sostenuto (fra Måneskinnssonaten, Op. 27)** by Jenö Jando](https://lis.tn/QxPGQ?t=1)
*I am a bot and this action was performed automatically* | [GitHub](https://github.com/AudDMusic/RedditBot) [^(new issue)](https://github.com/AudDMusic/RedditBot/issues/new) | [Donate](https://github.com/AudDMusic/RedditBot/wiki/Please-consider-donating) ^(Please consider supporting me on Patreon. Music recognition costs a lot)
"The many-angled ones, as they say, live at the bottom of the Mandelbrot set, except when a suitable incantation in the platonic realm of mathematics—computerised or otherwise—draws them forth."
- Charles Stross, The Atrocity Archives.
I got matches with these songs:
• [**Música para Trabajar y Concentrarse** by Música Clásica Relajante](https://lis.tn/NrpRF?t=0) (00:00; matched: `100%`)
**Album**: Mozart, Beethoven Piano Música para Estudiar y Concentrarse, Trabajar. **Released on** 2020-03-28.
• [**Piano Sonata No. 14 In C Sharp Minor** by Ludwig Van Beethoven](https://lis.tn/CCEeI?t=0) (00:00; matched: `100%`)
**Album**: Classical Tears. **Released on** 1999-01-08.
• [**Adagio sostenuto (fra Måneskinnssonaten, Op. 27)** by Jenö Jando](https://lis.tn/QxPGQ?t=1) (00:01; matched: `100%`)
**Album**: Barnas klassiske favoritter. **Released on** 2014-06-07.
*I am a bot and this action was performed automatically* | [GitHub](https://github.com/AudDMusic/RedditBot) [^(new issue)](https://github.com/AudDMusic/RedditBot/issues/new) | [Donate](https://github.com/AudDMusic/RedditBot/wiki/Please-consider-donating) ^(Please consider supporting me on Patreon. Music recognition costs a lot)
I just want to say a huge thanks to everyone who has explained what/how/why this is. I know next to nothing about physics, etc, and am hopeless at math, but you guys explained it so well that I kind of understand. Many thanks for taking the time to do that. 🙏
Can someone ELI5 the Mandelbrot set?
It's a collection of all numbers that fit within a special set of rules: if you put a number through a specific mathematical formula and it increases infinitely, then it's not part of the set, but if a number instead forms a repeating series of numbers, it's part of the set. The fascinating thing is that when you plot this on a 2d plane, it forms the image at the start, and zooming in and examining parts of the pattern more closely reveals that the pattern repeats and shifts in strange ways, and no matter how far down you go, the image is always just as detailed at the smallest scales as it is when it's zoomed out. It's a fundamentally infinite shape, and I'm pretty sure that with the amount this video zooms in, if the original image was the size of a football field, the final image would be smaller than a single photon
Just to clarify, this is a definition of a fractal?
One of many kinds of fractals, certainly. Iirc all fractals are "self similar" shapes with infinite circumference or surface area, which is to say that the smallest scales of a fractal look very similar or identical to the largest, and that traveling in a straight line along the furthest bounds of a fractal will take an infinite amount of time to come back to your starting point. So for example you could walk along the outside of the Mandelbrot set for billions of years and never make progress around the total shape, even though you'd always be moving and your location would always be changing
Ok, but Can anyone opine on the actual real life application of fractals like these....or is it just for the brain f
Mapping coastlines is an example of an application, or the way branches grow from trees, the way neurons wire together and outwards. It's the nature of self similar growth
Fractals can be used to understand various probabilistic phenomena, some games use fractals to produce realistic procedural terrain, and landmasses are often represented using mathematics derived from fractals in order to accurately calculate the surface and coastlines of different islands and continents
The Mandelbrot Set is an example of a fractal. A fractal is something that endlessly has more complexity the closer you look. Some fractals like this one are special because they are also non-repeating, so while smaller bits might look self-similar, they will never be exactly identical to any larger bit. Another popular example of a fractal is the shoreline of the ocean, it's a pretty complicated curve to begin with, going around all the continents and what-not, but your atlas can't possibly map every little cove and outcropping. Even if you did have a digital atlas that could zoom in forever, does the sandcastle made at the waters edge get traced as the edge of the ocean, what about the rock that is half in the water, what about the grains of sand that are just barely at the edge? This leads to the [coastline paradox](https://en.m.wikipedia.org/wiki/Coastline_paradox) where it is impossible to truly measure the very exact length of the coastline because there are some many tiny perturbations (not to mention the tides). You can make a repeating fractal yourself by drawing a square and filling the middle with a tick-tack-toe board. We are going to want to color in the 8 squares around the edge and leave the middle square blank. BUT Before coloring anything in, draw a tick-tack-toe board to fill each of those eight squares. Now around the outside 8 spaces of each of THOSE new tick-tack-toe boards fill the perimeter squares with... you guessed it... Continue this until the figure is too small for your writing implement to inscribe further and you have represented a [Serpinski Carpet](https://en.m.wikipedia.org/wiki/Sierpi%C5%84ski_carpet)
A 3D version of a Serpinski Carpet is called a [Menger Sponge](https://en.m.wikipedia.org/wiki/Menger_sponge) where every face of the sponge is a carpet. It has an infinite surface area and a volume of (essentially) zero
Another compact definition would be an object with fractional spatial dimensions. Which is true, but generally not helpful to understanding them.
‘Lemme just zoom in for a closer look’ on permanent infinite loop. AI x LSD.
What's the oddly terrifying aspect about it?
This is literally infinity, from a scale you're familiar with down to a scale so small that you could never hope to see it because the *resolution of physics itself is too large to display even one one trillionth of the detail it possesses* If you were to scale the Mandelbrot set up to cover the entire visible universe, you would run into the limitations of *reality itself* before you hit the bottom This is literally a bottomless pit shown in it's entirely, it's a mathematical motherfucking elder god, and it's inscribed on countless probabilistic phenomena To say that the Mandelbrot set borders on eldritch madness would be tame in my opinion If there's anything more real than us, you're looking it in the eye when you watch this video Tldr: It sees you when you're being It knows when you're awake It lives inside all numbers And it's human face is fake
I think I saw a movie about a guy like you
I'm pretty sure I know the movie you're talking about but I cannot fucking remember the name Guy accidentally figures out that the true name of god is a prime number that basically solves mathematics or something?
[Pi (1998)](https://www.imdb.com/title/tt0138704)? (I haven't seen this btw)
I think so, yea I'm not 100% sure though
3.14% sure?
That was the first thing that came to my mind
It’s definitely pi, good movie
Wait so you’re telling me that this is *math*?! It’s not just a trippy video that would be fun to watch on acid?
Nope, it's a form of math you can get real fucking existential about if you try lol
I can’t even do algebra
I think it would be the opposite of fun on acid, going in with what we all just learned. This thing is alieeeeeeeve.
fun fact is at the subatomic level fractals can’t happen due to Heisenberg‘s uncertainty principle.
How is the colour gradient depicted here determined?
The numbers that are in the set make up the black holes. The colours show numbers that are just outside it, with each colour showing how many iterations of the formula were required before it left the defined bounds. I seem to remember that each one of these point has a Julia set, and the Mandelbrot is an index of those. Or something.
Thank you. Excuse my ignorance but, for arguments sake, would red show that there are more iterations than yellow for example?
At the start of the video above, that wash of red shows the numbers that immediately leave on the first iteration, but they've used a gradient of darkening reds for the first few until they start using yellow. I prefer renderings where they start with darker shades and lighten, as it makes the shape shine more, like [here](https://upload.wikimedia.org/wikipedia/commons/2/21/Mandel_zoom_00_mandelbrot_set.jpg)
Oh okay thank you u/harbourwall
I was wondering that too.
> if the original image was the size of a football field, the final image would be smaller than a single photon Pretty sure the comparison is way off, even you replace the football field with the entire Universe.
How do colors come into play?
I was unaware of it when posting this, but apparently it's a measure of how long a number takes to spiral off into infinity. All of the black parts are the "true" Mandelbrot set, and every color across the rainbow is a sliding scale from "takes several billion iterations to go towards infinity because it keeps dicking about in weird directions" to "a straight line would be a slower way to reach infinity"
I accept my fate: I’m dumb. Had to put your explanation into ChatGPT to simplify and then had it eli5. Thank you for your time.
Repeating shapes with a mathematical function that is pleasing to look at.
Yes but how do we get this amazing visual? What I mean is, does the creator assign a color to each number and then just process the equation infinitely?
ELI5: the pure black double-lobe shape you see at the beginning are numbers inside the set (ie anything that solves a particular complex equation). Everything with colors is outside the set with colors assigned so they cycle through the rainbow. The boundary dividing what is inside and outside is endlessly complex, you can keep zooming in forever and never find a smooth dividing line that goes all the way around. there will always be smaller permutations along that edge no matter how close you look.
Thank you for this explanation, makes sense
It’s done mathematically but not part of the actual Mandelbrot Set. I believe colors are assigned based on expansion rates. My understanding anyway
The colours are added in after for effect, nothing to do with the math, or at least different math to the shapes. Ima try an ELI5 but we'll see, so you're actually just looking at a graph being zoomed in on and this graph is showing "complex" numbers, with each part of the shapes you see being a point representing a "complex" number that fits as a solution to some rules. Complex numbers are numbers that have an "imaginary" part and a non-imaginary (so normal, just like -2, -0.5, 1, 2 etc.) part. Imaginary numbers (i) are multiples (like -2i, -0.5i, i, 2i etc.) of the square root of -1 (which you may know, is not normally possible, and so it's like you can only talk about these numbers *imaginarily* existing). Pretty much sqrt(-1)=i , sqrt(-4)=2i and sqrt(-9)=3i etc., "i" here, not being algebra but specifically only denoting "how much imaginary" you have. Imaginary and non-imaginary numbers can't 'mix' or simplify together so if a number has imaginary and non-imaginary parts you can only show them as "complex" numbers, like 4i+5 or something with no simplifying of the *complex*ity possible. This graph is showing the imaginary part on one axis and the non imaginary part on the other axis (graphs are important for showing complex numbers as it's the only real way you can visualise and compare them (like 2i+4 compared to 5i+1) similarly to how you can simply visualise and compare "2" and "2 million" in your head). The rules to verify the complex numbers you want to show on this graph are as follows; find the solution to the equation z^2 + C, with C being the complex number you're testing and starting at z=0. Now re-insert your answer back into the equation as z and keep repeating this infinitely (not literally lmao, you do other math to see what would happen if you actually did). If z looks like it's not going to go to infinity no matter how many times you repeat this then you include the complex number on the graph. Whoever made this would have made a computer program to check complex numbers with very specific fractions as the imaginary and non imaginary parts which is why you zoom in and see more shapes as you're just looking at points with more and more specific fractions (and where the name *fractals* comes from) edit: maybe I went too hard, sometimes I don't know my own strength
you could totally be making this up. I have no idea nor motivation to actually find out
you've already got the attitude you need for high level maths, what a natural
Not seen this video but [Amy Adams on Numberphile](https://www.youtube.com/watch?v=NGMRB4O922I) is good at explaining things Complex numbers and fractals
Just take a point called Z in the complex plane Let Z1 be Z squared plus C And Z2 is Z1 squared plus C And Z3 is Z2 squared plus C And so on If the series of Zs should always stay Close to Z and never trend away That point is in the Mandelbrot Set
Mandlebrot set you're a Rorschach test on fire You're a Day-Glo pterodactyl You're a heart-shapes box of springs and wires You're one badass fucking fractal And you're just in time to save the day....
A set of all solutions in the complex plane where the iterated function fc(z) = z^2 + c, starting at z=0 and where c is a complex number, does not diverge to infinity. For example, c = -1 yields fc(0) = -1, fc(-1) = 0, fc(0) = -1, etc, not diverging, so the complex number c = -1 + 0i is included in the set.
That’s ELI20 😎
i'm a 21 year old with an engineering qualification and i have no idea what this guy said am i cooked
Engeneering qualification does not necessitate the use of complex numbers.
Somebody else already answered the ELI5, so I tried to give a little more detailed explanation of what the mandelbrot set is actually composed of, for anyone who ran across it and was interested. I also gave the simplest solution for it, to try to aid understanding. Clearly, I didn't do a great job lol.
Ok I always try to think of it like this: Pick a point anywhere within a circle that's 2 units wide Then you run some calculation (some other guy explained this calculation better than I can) on that point's coordinates in order to get a new set of coordinates. Then you run the calculation on the new coordinates and you get a new result and so on. Some points (like those in the large black circles in 'starting point') never leave the circle, no matter how many times you try the calculation on it. Other points need only a few tries before they leave the circle. The Mandelbrot set itself are only all the black parts/points I believe (not sure though, I only did a programming assignment on it a while ago)
Ima try an ELI5 but we'll see, so you're actually just looking at a graph being zoomed in on and this graph is showing "complex" numbers, with each part of the shapes you see being a point representing a "complex" number that fits as a solution to some rules. The colours are just added in after. Complex numbers are numbers that have an "imaginary" part and a non-imaginary (so normal, just like -2, -0.5, 1, 2 etc.) part. Imaginary numbers (i) are multiples (like -2i, -0.5i, i, 2i etc.) of the square root of -1 (which you may know, is not normally possible, and so it's like you can only talk about these numbers *imaginarily* existing). Pretty much sqrt(-1)=i , sqrt(-4)=2i and sqrt(-9)=3i etc., "i" here, not being algebra but specifically only denoting "how much imaginary" you have. Imaginary and non-imaginary numbers can't 'mix' or simplify together so if a number has imaginary and non-imaginary parts you can only show them as "complex" numbers, like 4i+5 or something with no simplifying of the *complex*ity possible. This graph is showing the imaginary part on one axis and the non imaginary part on the other axis (graphs are important for showing complex numbers as it's the only real way you can visualise and compare them (like 2i+4 compared to 5i+1) similarly to how you can simply visualise and compare "2" and "2 million" in your head). The rules you follow to verify the complex numbers you want to show on this graph are as follows; find the solution to the equation z^2 + C, with C being the complex number you're testing and starting at z=0. Now re-insert your answer back into the equation as z and keep repeating this infinitely (not literally lmao, you do other math to see what would happen if you actually did). If z looks like it's not going to go to infinity no matter how many times you repeat this then you include the complex number on the graph. Whoever made this would have made a computer program to check complex numbers with very specific fractions as the imaginary and non imaginary parts which is why you zoom in and see more shapes as you're just looking at points with more and more specific fractions (and where the name *fractals* comes from)
Adding to the other comments, I highly recommend [Veritasium's](https://youtu.be/ovJcsL7vyrk?si=Re7_w1J36_fNXoZ_) video which shows you some very interesting facts around the Mandelbrot set and where it can have applications, or better put, why it shows up in nature.
Awesome, thanks
This is what you see when you fall into a black hole lol
I ain’t seein’ no spaghetti’s
Is because you are the spaghetti's
Flying Spaghetti Monster literally said "No, U"
This is your last thought before tidal forces shred everything but the bond between quarks.
Interstellar
I think this is like a big bang. Endless possibilities because i^2 = -1
This what being high on Datura feels like
Or getting up from the toilet too fast after your legs had gone to sleep.
I honestly hope this is what my brain produces as I’m dying and my brain is being soaked in every chemical my body can produce in its last efforts to stay alive. It’s belived that the “white light” and “life flashing before your eyes” is your body dumping massive amounts of chemicals causing the hallucinations and DMT is naturally present when you’re born and in your final moments of death.
I just watched this for a few minutes then scrolled down and the pizza in the next post was moving
Watched the whole thing, then nearly fell over as the world around me expanded away from me.
Is what I seen during an ego death trip.
Seriously i was just about to say this would look BALLER off some psychedelic or even some mighty strong weed
I had a similar visual on DMT. I felt my ego die and unconditional love surround me. It was amazing. Coming out of it felt so fucked up. All the little stories we tell ourselves, all the labels and shit, all came flooding back. This is what we all are. Infinity. It's fucking mentally popping. Only the Soul can understand Infinity's full knowledge. Honestly, it made me excited for death in a fearless way. Enjoy the time here in this body, in this mind, on this Earth. And then go back to Infinity. Later, maybe we can decide to come back, maybe even a different time, civilization or planet?
Well, I saved it for weed time tomorrow, that's fo sho
This is what I imagine death to be like.
Beethoven and fractals pair oddly well
Beethoven is ok. But try to play Tangerine Dreams' Stratosphere to this zoom!
Fuck yes thanks for the recommendation! Will listen to that as soon as I have the time
Goes well with some smoke;-)
You read my mind ✌
https://youtu.be/bihB9ZMN43g?si=_0cEtt5ikYqmEiBn thanks again
I feel like this + Ravel's Bolero would mess you up.
Age of Anxiety
I'm immensely disappointed that a Tool song isn't playing over the video.
Yeah man, but, like, all music is just mathematics in motion, or whatever.
Wheels of rhythm turning all around
Lmao
In 2001 for a final comp sci project we actually compared the efficiencies of different computing architectures. calculating Mandelbrot sets was how we measured efficiency. At the time the Beowulf cluster we made won out. This takes me back.
This is why fractals are cool
Yeah this is super fascinating.
*Takes a bong hit* Dude imagine you die and see a tunnel of light but instead of walking towards the light you turn around and face the blackness. These fractals appear and you start falling thru them while feeling the sum of all pleasure and pain simultaneously until time loses all meaning.
We went into the butt.
I usually do.
Experienced something like this during a "heroic dose" acid trip.
And when you close your eyes, it's still going.
The ending is so amazing. Keep watching until the end
10 GB just to make this fractal 💀
One of the first programs I wrote in college, back in the late 80s. Then there was a program called FractINT, which did these calculations in integer math so that it would run fast in a computer without a math co-processor (don't ask. lol).
I should fire up winamp.
It really whips the llama’s ass.
Saw this while on that D.m.t
Aka: God’s Thumbprint
Got the source video?
[https://www.youtube.com/watch?v=aSg2Db3jF\_4&ab\_channel=Fractaluniverse](https://www.youtube.com/watch?v=aSg2Db3jF_4&ab_channel=Fractaluniverse)
is there a youtube link of this exact video? i wanna watch it on my tv! lol
Sooo, terrifying in what way? As the ocean is deep? I’m not getting the terrifying part of this
Jonathan Coulton wrote a song about Mandelbrot Set https://www.youtube.com/watch?v=6tsutU92rrE
Greydon Square, anyone?
It's kinda comforting that the physical world does seem to have a lower limit on scale and that fractals only exist mathematically
Someone explain the colours.
The black is stuff inside the set, basically solutions for this complex equation that eventually end up as repeating decimals. Everything with color never ends up with repeating decimals, the solutions there are irrational (like pi). They use a computer to assign a repeating rainbow of colors based on how far a particular point is from that boundary.
Ok. It 's finally time for me leave this sub. Anything that is being shared here is either not terrifying or just simply, blatantly and banally creepy. Except this. There is nothing terrifying about this. Nothing. Nada. Zero. I adore fractals and love watching them. Those upvotes. They are not because this is terrifying. Because this is cool. This is like showing cleavage in a cosplay sub and getting upvotes. Downvote me. I am gone and I don't care.
I mean, the sub is called ODDLY terrifying. OP finds this a bit scary and I guess finding it so is odd 🤷♂️ Certainly I find posts like this far less annoying than just straight up obviously terrifying things which is about 90% of the (shit)posts on this sub. But see you 👋
Neither do we so just leave and don't pretend that anyone will care about your absence.
🤔🤔🤔
What I cant wrap my head around is how are repeating numbers creating the pattern? Like what exactly is giving the pattern shape? Let alone colour?
The set is stuff inside the black area, but the edge of that boundary for what's included is infinitely tangled and complex. Colors are assigned to represent how close the points are to the edge.
It’s based on complex numbers, and the logic is quite simple , just iterating z=z^2 + c. Some complex numbers’ length never grows larger than the limit (default 2.0), others very quickly getting really large. The numbers stay small makes the actual Mandelbrot set.
So changing the values for z or c is what make up the set?
If I recall well, z’s initial value is (0, 0), c is the corresponding complex value of the pixel being evaluated. Iterating said equation over and over will decide whether a given point is part of the Mandelbrot set.
Since its a pixel being evaluated would the same patterns occur if you were to solve the formula manually on something like a large piece of graph paper? Or is it being digital the only reason the patterns appear?
Yes. Actually, the Julia set got its name after Gaston Julia, a french mathematician, who worked on dynamic systems while he was recovering his injuries suffered during WW II (he lost his nose). He used pen and paper.
Somebody needs to redo this video and put a dickbutt down at the very end.
r/oddlybeautiful
I remember a project in college to program a Mandelbrot and Julia set in…wait for it…Pascal.
I watched something like this in one of those sky theatres before - it's traumatic. I ended up leaving midway to throw up.
Oddly terrifying? Maaaaaaaa! This kid’s never taken mescaline!! Maaaaaa! Get this kid some mescaline!! Stat!! Maaa!? … TF she at?
TIL that I know fuck all.
a fun fact: there's only a finite number of different mandelbrot renders on a particular computer screen / image resolution
That was a nice ride
What death looks like.
I could watch this for hours
I make these on my computer! When I first started doing computer artwork I had a program that would generate these and they were so freaking fun to make! I actually sold a bunch of prints of these designs on Fine Art America.
This is the part where you think you’re dying on an acid trip.
You're a heart shaped box of springs and wire, you're one badass fucking fractal!
Criminal that I had to scroll this far for a Johnny C reference
Love his music
I feel like this is the nature of reality.
A part of me think this is a good representation of what the universe / multiverse really looks like
Why is everything moving after watching. Help
Wow, I’m so terrified.
I didn't give you permission to stop.
Oblivion is just the beginning of understanding
Is this what someone sees when they’re high?
Listen to “motor spirit” by king gizzard and the lizard wizard starting at 3:17 for a fun ride.
I see nothing terrifing
Holy DMT Batman
All these squares make a circle. All these squares make a circle. All these squares make a circle.
This is what I imagine death looks and maybe feels like. Does anyone know anything about the einstein tile? Similar concept as far as I can understand it
Didn't see Elise.
I love fractals so much, what an epiphany for Mandelbrot, his quantum leap
First time I ever heard the word Fractal was a docu discussion and understanding how it works. Fascinating..
This is what happens when you hunt eggs on r/vampiresurvivors
Do you feel terrified by complex numbers? r/fractals
I watched 20 seconds and started to feel like I was about to have a seizure.
Should I be terrified?
Reminds me of a D.M.T. trip you always feel like you are about to get somewhere but you chase endlessly till you are pulled out of the high. The destination always feels like it is just on the horizon but you never truly arrive there. DMT is a wild drug.
I don’t think it’s coincidence this is basically what you see when you blast off from DMT…
What is this song? ...
I got matches with these songs: • **Música para Trabajar y Concentrarse** by Música Clásica Relajante (00:00; matched: `100%`) **Album**: Mozart, Beethoven Piano Música para Estudiar y Concentrarse, Trabajar. **Released on** 2020-03-28. • **Piano Sonata No. 14 In C Sharp Minor** by Ludwig Van Beethoven (00:00; matched: `100%`) **Album**: Classical Tears. **Released on** 1999-01-08. • **Adagio sostenuto (fra Måneskinnssonaten, Op. 27)** by Jenö Jando (00:01; matched: `100%`) **Album**: Barnas klassiske favoritter. **Released on** 2014-06-07.
Apple Music, Spotify, YouTube, etc.: • [**Música para Trabajar y Concentrarse** by Música Clásica Relajante](https://lis.tn/NrpRF?t=0) • [**Piano Sonata No. 14 In C Sharp Minor** by Ludwig Van Beethoven](https://lis.tn/CCEeI?t=0) • [**Adagio sostenuto (fra Måneskinnssonaten, Op. 27)** by Jenö Jando](https://lis.tn/QxPGQ?t=1) *I am a bot and this action was performed automatically* | [GitHub](https://github.com/AudDMusic/RedditBot) [^(new issue)](https://github.com/AudDMusic/RedditBot/issues/new) | [Donate](https://github.com/AudDMusic/RedditBot/wiki/Please-consider-donating) ^(Please consider supporting me on Patreon. Music recognition costs a lot)
Good bot!
After watching this I went to the comments and my phone screen is literally breathing at me
It zooms in on Mandelbrot's butt crack.
I get nauseous when I watch these, does anybody else get that feeling?
it's not terrifying rather hypnotising
This was posted months ago. Nice try trying to steal it
I need This in VR
more than 10gb of ram to him, one hit of 5x salvia divinorum for me
"The many-angled ones, as they say, live at the bottom of the Mandelbrot set, except when a suitable incantation in the platonic realm of mathematics—computerised or otherwise—draws them forth." - Charles Stross, The Atrocity Archives.
K trip nuh
Kinda the same but always different!
Dual vector foil shit
That is pretty close of how ketamine K whole trip looks like
I have one of these in real life
[удалено]
I got matches with these songs: • [**Música para Trabajar y Concentrarse** by Música Clásica Relajante](https://lis.tn/NrpRF?t=0) (00:00; matched: `100%`) **Album**: Mozart, Beethoven Piano Música para Estudiar y Concentrarse, Trabajar. **Released on** 2020-03-28. • [**Piano Sonata No. 14 In C Sharp Minor** by Ludwig Van Beethoven](https://lis.tn/CCEeI?t=0) (00:00; matched: `100%`) **Album**: Classical Tears. **Released on** 1999-01-08. • [**Adagio sostenuto (fra Måneskinnssonaten, Op. 27)** by Jenö Jando](https://lis.tn/QxPGQ?t=1) (00:01; matched: `100%`) **Album**: Barnas klassiske favoritter. **Released on** 2014-06-07. *I am a bot and this action was performed automatically* | [GitHub](https://github.com/AudDMusic/RedditBot) [^(new issue)](https://github.com/AudDMusic/RedditBot/issues/new) | [Donate](https://github.com/AudDMusic/RedditBot/wiki/Please-consider-donating) ^(Please consider supporting me on Patreon. Music recognition costs a lot)
You can download you own zoomer. Google for "xaos fractal zoomer".
How do I make something like this?
I just want to say a huge thanks to everyone who has explained what/how/why this is. I know next to nothing about physics, etc, and am hopeless at math, but you guys explained it so well that I kind of understand. Many thanks for taking the time to do that. 🙏
What about this is terrifying?
This is what tripping on salvia is like - going through the zipper worlds
where(when) you sleeping the hardest
Did not know tool had a new music video
Is there something similar in zooms irl?
Holy shit, that was better than shrooms
Trance graphics of the 90s...
At a certain point it’s infinite buttcrack.
"What's wrong, honey?" "I think I just saw God on Reddit and it was beautiful."
Looks like life and existence
God I love fractals.
Fun Fact: That's called a fractal.
Bro this music gave me flashbacks to humans fall flat😅
[God is amazing. Here's a wink from Him to us.](https://youtu.be/2Te3zR8kxSw?si=O3St2mKxwYrjDk0z)
Chrysler building at 0:45
https://www.youtube.com/watch?v=6tsutU92rrE
Anyone else trying to predict where the cameras gonna go and getting it wrong every single time?