The paperCrane’s view from the reverseFold

On the way home last Thursday I decided to try creating fractal letters. The idea was to replace each “line” in a simple version of a letter with a copy of itself but allow for the aspect ratio of its dimensions to change so that the result is still recognizable as a letter. This is something like an L-system, of which the Dragon curve is one. After a weekend’s worth of work I have what amounts to thirteen different fractal letter algorithms for six different letters. 1 P, 3 A, 2 E, 2 R, 2 C, 3 N. Yes, those spell PAPERCRANE. Here is the first iteration (just the letters).

Fractal Letters, iteration 1

And here is the fifth iteration:

Fractal Letters, iteration 5

Some letters have variations in how they are drawn or how they repeat, or both (hence the 2 lines). The bottom N uses an algorithm I worked out which didn’t change the aspect ratio and had only one repetition per line. Both of the N variants in the words use two repetitions per line and constrict the width faster than the height, which leaves the N recognizable. The idea here, after all, was to make letters which had a cool fractal look but could still be read.

Click either of the pictures to view the flex app and play with the iterations yourself. Just drag (or click on) the slider on the bottom of the app to change the iteration.

Stay tuned, I have another blog post coming up soon specifically about that N on the bottom, the math required to create the algorithm, and some interesting (and beautiful) results I got when implementing a test program.

Let’s keep the ball rolling with another fractal creation. I’ve been playing with Papervision3D lately due to its use in a recent site I worked on and the San Francisco Papervision3D class I attended a few weekends ago. This latest is a verson of the sierpinski gasket which follows the same ideas as the last one I made but using 4 points to make a tetrahedron in 3 space. The same symmetry is applied but 4-fold and the lines are drawn but soon after removed as they quickly overshadow the pixels and slow the rendering down quite a bit once there are more than a few. Also notice that the pixels have some nice effects applied to them, making a kind fo vortex. Thanks to Andy Zupko for the Effects branch of Papervision3D and his part in the class I attended.