The paperCrane’s view from the reverseFold

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.