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Some extremely epic art derived from maths

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Well, not sure how I found myself on this webpage (I think I only slept for 3 hours or less last night, maximum), but anyway, I've never felt such a strange combination of extreme happiness and inadequacy. If you like what Xenodimensional does, then you will like a lot of this stuff too.

http://gallery.bridgesmathart.org/exhibitions/2012-bridges-conference

I don't really see much point in posting over a huge selection of what's there, but if you find anything awesome, post your favourite. :)

Here are some of my favourites:

simple_as_the_number_nine.jpg

by Kerry Mitchell

This one is made of the chaotic orbits of bounday points of the Mandelbrot set. This if the Mandelbrot set for those who forgot:

322px-Mandel_zoom_00_mandelbrot_set.jpg

structure_1..jpg

by Alexandru Usineviciu

This one is not that beautiful compared to some of the others. But there's so many ideas it contains. All he did was use twisted wire pieces, and "weave" them together by "screwing" each wire piece in (there's no knots or welds).

The last one is my most favourite, and it's called the Electric Sheep, and it's by Scott Draves. It's the one that's just so amazing, that I can't help but feel like a lesser human being in it's presence. The artwork is a distributed computer program that generates artworks through evolutionary design and participation of users (you "vote" for what you like, and the one you voted for gets to evolve). I'm sure I haven't explained it well at all. But it's just amazing to marvel at the individual pieces that it makes, and how original they all are. Here's a sample:

electricsheep.244.48405.png

electricsheep.244.20617.png

electricsheep.244.20568.png

And there's just so many more: http://v2d7c.sheepserver.net/cgi/best.cgi

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wow, that second link is awesome!

simulations of turbulent fluid structures can generate some pretty awesome art too:

stellar.jpg

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Electric Sheep

First created in 1999 by Scott Draves, theElectric Sheep is a form of artificial life, which is to say it is software that recreates the biological phenomena of evolution and reproduction though mathematics. The system is made up of man and machine, a cyborg mind with 450,000 participant computers and people all over the Internet.

This is a distributed system, with all participating computers working together to form a supercomputer that renders animations, called "sheep", that everyone sees. The human participants guide the survival of the fittest by voting for their favorite animations in the flock. You can join this project by downloadingthe Electric Sheep Screensaver.

Each participating computer follows mathematical instructions, Draves' Flame algorithm, to render its own piece of the larger work, as seen in the table at left. The images are sent back to a central server which compresses them into animations which are sent back out to the viewers. The electricsheep.org website shows the family tree for each sheep, including its parents and offspring, and viewers can track family resemblance. The artist's Clade series shows a selection of family members in high resolution.

Like Draves' other software art, the Electric Sheep code is open source, which has allowed it to benefit from code contributions from many enthusiastic programmers. Now Draves serves as head Shepherd on a project with many participants.

The most popular sheep from the current flock can be viewed on the live server, or you can browse the archive

that is really cool, especially the genetic algorithm part. amazing that something so apparently rigid such as computer code, with input from human 'intelligence' via the selection process, can generate such beautiful images. it goes some way to convincing me that a scientific/mathematical description of reality does not take away its beauty, quite the opposite really. if such complex images can be formed simply by enormous numbers of iterations on simple equations, then maybe its entirely possible life as we know it evolved purely out of the billions of years of iterations the universe has produced? but these images required human input to select the best features, what is the equivalent in the universe?

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i'd like to see some algorithmic art on embedded chips connected to a lcd screen or something, to replace traditional paint paintings. like you could have a menu, setup parameters and then leave it grow and watch it grow over like a week or something, evolving art.

Edited by qualia
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Yeah, I think that it's something like that as well. Part of the problem with imagining evolution is just the timescale involved. Here's the best way I know to represent the insane time-scales involved:

Time_Clock.gif

Just to give a reference, dinosaurs went extinct about 65 million years ago. Humans evolved about 300,000 years ago (to put a number on such a thing is mildy pointless, as it was a continuous, but bumpy process). So written history (which began about 10,000 years ago roughly), didn't start until about 2.5 seconds until midnight. That's about the same time that most Woolly Mammoths died out (although I just learned some survived for another 6000 years on a small Russian island - cool, I'll go and visit one day maybe).

In terms of beauty, I don't think it exists as an absolute - i.e. things exist, and we call the things we find something pleasing; beautiful. It really only takes one google image search of "Polypropylene implants" to get an idea that not everybody shares the exact same flavour of beauty. I don't think the universe selects for beauty, but that we find beauty in what the universe selects. ^^

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*googles "Polypropylene implants"*

YIKES! :blink:

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Qualia, have you heard of Conway's game of life? It's a bit like Minecraft, but more simple and more complex.

Here's a video (that impossibly only has 2400 views; at the bottom), that shows a self-replicating mathematical structure. It's almost intelligent. Here's a rough intro. Basically, you have a grid. And each grid square can either "alive" ("on"), or "dead" ("off"). The grid is meant to be infinite. So far pretty simple. Now there's four more rules:

  1. Any live cell with fewer than two live neighbours dies, as if caused by under-population.
  2. Any live cell with two or three live neighbours lives on to the next generation.
  3. Any live cell with more than three live neighbours dies, as if by overcrowding.
  4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

So you set up your initial configuration of dead and alive cells, and step back, and let the rules do all the work (as in once you've placed the initial alive and dead cells, there's nothing else you need to do).

So in the beginning, they found all these little patterns. They used to do it manually with a Go board, but eventually it made its way to the computer.

These ones have a period of 2. As in every 2 game cycles, they are repeating.

Game_of_life_blinker.gifGame_of_life_toad.gifGame_of_life_beacon.gif

These ones stay the same forever (until their neighbours change):

98px-Game_of_life_beehive.svg.png98px-Game_of_life_loaf.svg.png82px-Game_of_life_boat.svg.png

Then they found these patterns which "moved" all by themselves across the grid:

Game_of_life_animated_glider.gifGame_of_life_animated_LWSS.gif

So here's where things get more interesting. They managed to combine patterns to create the moving patterns (i.e. to "shoot" the self-moving ones):

Gospers_glider_gun.gif

Here's another higher-level shape; it's actually shooting out shooters, that then shoot flyers.

Conways_game_of_life_breeder_animation.gif

So remember, all of these are made by following the rules through in a turn-based manner. Nothing else.

Then as people managed to combine the simpler blocks into the more complex blocks, we get a self-replicating pattern. It's just insane that someone would go to so much effort, but still amazing. Btw, that long "line" going to the bottom right is it's "DNA", that it reads in order to make itself (the new "itself" can also make a new "itself")

The key thing to me is just how simple the rules are.... It seems the simpler the rules, the greater the possibilities. The rules for chemistry are pretty simple as well.... :D

Edited by βluntmuffin
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^ nice animated gifs. it requires a very specific initial condition to generate that "shooter" example, I wonder how they went about working that out? :scratchhead:

In terms of beauty, I don't think it exists as an absolute - i.e. things exist, and we call the things we find something pleasing; beautiful. It really only takes one google image search of "Polypropylene implants" to get an idea that not everybody shares the exact same flavour of beauty. I don't think the universe selects for beauty, but that we find beauty in what the universe selects.

yeah I think your right, there is something innate in humans that finds certain patterns the universe produces beautiful. beauty is a really interesting thing. why do we find fractals so aesthetically appealing? why do psychedelic experiences involve cascades of patterns that we find beautiful? projected onto another person, beauty can be explained to have an evolutionary advantage in that it is a vector for finding the most appropriate sexual partners for us. we all have different genetic makeups, so we all theoretically should be attracted to different types of peoples, and we are. so if beauty has a purpose, why is it important for us to find abstract art like this beautiful? perhaps the universe wants us to understand and make use of certain patterns, so as to create a more streamlined existence.

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