I’ve continued adding bits to my fractal letters over the past few weeks and have finally finished everything to print out my full e-mail address. The @ symbol was particularly interesting and I think it turned out pretty nice.
Fractal Email - first iteration
Fractal Email - third iteration
Fractal Email - fifth iteration
The pictures link to the updated app. Enjoy, and as usual, don’t slide the slider up to the max unless you’re willing to wait while your entire browser hangs for several minutes.
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.
Ever snce I got my tattoo(s) I have been explaining the fractal known as the dragon to anyone who takes an interest in it. I’ve even named some of my villages in Travian after the turns you take to create some of them. While explaining the fractal yet again I remembered the way that I originally learned to build it: draw the next iteration over the old one. I originally found this fractal at the beginning of each chapter in Jurassic Park. Since it had a regular box shape I used to use graphing paper to draw it, then after time realized that I could turn the paper over and draw the next iteration over the old one using a simple algorithm. Start by drawing a right angle to one side of the first line, then draw a righ angle to the other side of the next line, and repeat. I have programmed this fractal many times before but I had never actually coded up this algorithm before. I also wanted it to animate so as to show the drawing steps. Without further ado:
While on the plane back from Indianappolis I had two new ideas for generation of a Sierpinski Gasket: 3-way symmetry and line display. For those that don’t know what a sierpinski gasket is, it is a fractal that starts as an equilateral triangle with another one inscribed inside it. The next iteration adds triangles inscribed in the 3 “edge” triangles. This continues over and over (forever).
This implementation uses a different method of generation. You start at a random corner of the triangle, choose a random corner, move halfway to it, and draw a dot. Continue to randomly choose a corner, move halfway to it, and draw a dot, and you get the same thing as above.
