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You should explain what kinds of fractals these are (are they L-systems?) and how you go about crossing them.
by fogleman 7y ago
You should explain what kinds of fractals these are (are they L-systems?) and how you go about crossing them.
- atum47 7y agoI'm kinda promoting the book playing with chaos, I think people would learn better from it. Anyways, here's a link to a video from the author himself https://youtu.be/e0JaZuLfZ_0 https://youtu.be/e0JaZuLfZ_0
- danwills 7y agoIt's IFS (Iterated Function Systems): https://en.wikipedia.org/wiki/Iterated_function_system https://en.wikipedia.org/wiki/Iterated_function_system IFS uses a set of affine transformations (translation, scale, rotation and shear, which can each be represented by a single matrix, and in the 2d case you can think of them as a set of rectangles/parallelograms). IFS are most often drawn by starting from a random location and then repeatedly selecting a random transform from the set, applying it to the previous position and then drawing a dot at the new position. You can also generate all the locations first (yielding a point-cloud) and then rasterize them to make an image. The same idea applies using 3d affine transforms with almost no extra effort. I think this is what Richard 'doc' Bailey (may he rest in peace) may have been doing in his awesome 'image savant/spore' work. Flame fractals (electric sheep) extended the same idea with non-linear transformations, and coloring methods to great effect! There is also some cool formulas in the isosurface-based 3d-fractal scene (one is called 'Kaleidoscopic IFS') where the drawing method is (of course) very different but the underlying repeated-transformation principle is the same. Indeed most kinds of fractals can be thought of in the same way: Repeatedly apply some geometric transformation or deformation (or synthesis in the case of 'fractal noise') in feedback.