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GaulerTheGoat

Is it fractals?

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Hey all, I accidentally made these images in PSP7 and they look a lot like fractals, but I'm not sure what type they are or even if they are. Sorry about the clickies, too, but yahoo is the only web space I have (maybe someone can upload them to a better server). Images The images were created by starting with a white 200x200 canvas. Go to Effects->Noise->Add Noise=50 Random Go to Effects->Plug-in Filters->Eye Candy 3.1->Jiggle Twisty and repeat the twisty over and over again while the image slowly forms on the edges of the canvas. BTW, the jpegs are fuzzier than than the originals due to compression. I don't know much about fractals or what algorithm "jiggle" uses. Any comments? edit=oops. got the index up. [edited by - GaulerTheGoat on October 20, 2003 7:43:30 PM]

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Looks like a fractal. It looks like the ''jiggle'' effect is a midpoint displacement with rotation, which in theory could be continued recursively forever on smaller and smaller divisions.

It''s more or less the same idea as fractal-generated heightmaps for terrain.

Tom

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Guest Anonymous Poster
For it to be a fractal it would be possible to zoom into the picture indefinitely and see more and more details of the "jiggles".

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Another way to make a fractal in PSP (or any other suitable image editor) is to perform repetitive folding. Much like a taffy machine folds taffy.

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ParadigmShift:
I tried googling for ''midpoint displacement rotation'' and found this, except they call it plasma fractals. When I made the images, all the development is on the edges, slowly growing inwards. The center of the image changes very little. The "midpoint" would seem to be OK on the edges but isn''t there also supposed to be a 5th midpoint in the center of the other four? Maybe ''jiggle'' is a variant that doesn''t use the middle point? I''m going to try ''jiggling'' some simple shapes to figure out what''s going on. Thanks for the starting point.

AP:
Yeah, that''s why I don''t know if it''s really a fractal or not. It looks like one but of course, the details are being lost because we can''t see any deeper than one pixel.

Mastaba:
Sounds cool, but could you explain ''folding'' please? Googling for ''image folding'' got me, like nowhere

Thanks for replies

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For a simple folding map try googling for
folding map chaos

or

horseshoe map

They are quite complicated to study ( you''ll find them in post-graduate maths books )

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A fractal is a self-similare mathematical object that involves a repeated process over the course of, typically, an infinit amount of iterations and that retains a constant level of detail irrelevant of the amount of "zooming in". Of course, infinity isn''t something quite feasible on a computer

Here''s an example, an L-system (Lindenmayer system). Take a triangle. Now draw an inverted triangle in the middle of that triangle such as that the three points are the middle of the three sides of the initial triangle (think Triforce from Legend of Zelda). Color that black. For the remaining three triangles, do the same. You should have 9 triangles now. Keep doing that over and over. You''ll end up with a fractal object (the Sierspinsky triangle).

An other fractal, more well-known, is the mandelbroth fractal. Applying the equation z -> z² + c over a complex plane from -2-2i to 2+2i and coloring pixels which never escape a certain threshold black and the others white will result in a rather strange shape somewhat like a twisted sideways 8. Successive zooms into the image will reveal astounding details and a very self-similare structure (well, in fact, you''ll find the basic starting image all over the place).

So no, that''s not a fractal. It''s kinda nice though.

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quote:
They are quite complicated to study ( you''ll find them in post-graduate maths books )


Post Graduate! They were part of my undergraduate degree! Modern Analysis, Dynamical Systems, and Ergodic Theory all covered one or other of them.

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quote:
Original post by Keem
They are quite complicated to study ( you''ll find them in post-graduate maths books )


I wouldn''t really call ''em complex... The basics of it are quite simple. The actual philosophy behind them is rather... "heavy", as it is.

There''s a great book on the subject (well, chaos theory in general) that I consider my personal bible: "CHAOS - The Making of a New Science" by James Gleick. Very, very interesting read. Worth a look if you have the time.

It offers a really nice explanation of fractals, though.

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quote:
Original post by RuneLancer
Here's an example, an L-system (Lindenmayer system). Take a triangle. Now draw an inverted triangle in the middle of that triangle such as that the three points are the middle of the three sides of the initial triangle (think Triforce from Legend of Zelda). Color that black. For the remaining three triangles, do the same. You should have 9 triangles now. Keep doing that over and over. You'll end up with a fractal object (the Sierspinsky triangle).

Yeah, I've seen that before. And I like your Zelda reference. More mathematicians should play video games
Seen the Mandelbrot[h?] set, too.
quote:
Original post by RuneLancer
A fractal is a self-similare mathematical object that involves a repeated process over the course of, typically, an infinit[e] amount of iterations and that retains a constant level of detail irrelevant of the amount of "zooming in".
[....]
So no, that's not a fractal. It's kinda nice though.

I didn't know that in addition to having "infinite detail" (what's the mathematical definition of this, anyway? The boundry has infinite arc-length, or something?), it also has to have similarlty to itself (like at any neighborhood? Because the Mandelbrot looks different at different places.)

Why does this mean that the 'jiggle' images couldn't be fractals, though. They seem to be developing infinite detail (although, there's no way to tell without knowing the 'jiggle' algorithm). Also, the Mandelbrot doesn't look the same everywhere (it's lopsided, to begin with) so I'm not sure what you mean by self-similar (like, it maps to itself linearly, I think is the word?) edit="affine" map was the word I was looking for

When done on simpler objects, the 'jiggle' just looks a distorted expand and contract. It does it at all points, even the center (so I'm not sure why the center of the above images is unchanging).

When done on a straight line, eg, it looks like a really sloppy sine wave. But, if you do it on two perpindicular lines, they both look like perpindicular sine waves. Also, with some other experiments, it looks like the 'jiggle' is always perpindicular to the line (more or less).

Isn't there a fractal that starts out as a triangle, then the middle one-third of each straight edge is replaced with another triangle, and so on. Could the images above be formed by something like that, since it seems to have a similar kind of "straight line deformed by perpindicular motion" thing going on. This is just speculation, though

Thanks for good replies. You guys obviously know quite a bit about this stuff

[edited by - GaulerTheGoat on October 21, 2003 6:07:27 PM]

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