Mon, Sep 23, 4:23 AM CDT

My first post: Binary tree

Other Apps Fractal posted on Nov 26, 2011
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and seemingly it´s also the first one with such a strange genre/gallery-combination. I wanted to have some actually computer-generated, rendered image to post for my first time. The binary tree is certainly the most classical fractal, however, I wanted it to look more like a real tree, more dense. That´s why the elments are not shortening by a factor of two from level to level, but only by the squareroot of two. If you start drawing in kartesian coordinates, this has the further advantage that the distances stay even. Either coordinate doubles each second step. The diameter of an element changes from root to tip by the same factor. This way, there are no gaps between the elements. However, the shortening factor alone proved not to be enough when extending to three dimensions. So I decided to place four twigs on each branch and to turn them by 45°, making them point in every direction. The figure stays entirely self-similar; only the colors of the trunk, branches, twigs and, if you want to to call them so, leaves or needles are just "artistic", not following any mathematic rule. I wanted to look it like a tree. The image has been drawn and rendered with AutoCAD 2002 on a seven year old Windows-2000-PC, then grabbed and saved with Corel Photopaint 7, no further postwork. These are surely not state of the art tools, however, I doubt that they are the limiting factors. As the number of elements increases by a factor of four each recursion level, I ended up with 9 levels or 87000 elements, almost completely blocking my computer for about two hours. The maximum swap file size (2Gb) revealed to be the main limitation.

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