In this project I create all sorts of fractals. The main challenge I encountered was the optimization of the zooming into the fractal. I now make initial calculations for bigger squares first, reducing the amount of calculations necessary when zooming in. When the zooming stops, I render all intermediate pixels. When zooming with the mouse wheel, the zoom follows the position of the mouse exactly. This makes the experience quite nice.
The fractal created by the Mandelbrot set is the best known fractal in the world. The Mandelbrot set consists of all complex numbers c for which the function fc(z) = z2 + c does not diverge, when iterated with initial z = 0. This set is completely white in the fractal below. The colors signify the rate at which the numbers that are not in the set diverge.
Move around: arrow keys or mouse drag and drop
Zoom in and out: mouse wheel
Color change: A and Z (red value), S and X (green value), D and C (blue value), or P for party mode!
The fractal created by the Julia set has many similarities to the Mandelbrot fractal. Here too, the colors signify the rate at which numbers diverge and numbers that are in the Julia set are one specific color. The function that we use is also very similar, but the elements of the Julia set are the complex numbers z for which the function fc(z) = z2 + c does not diverge. This set is different for every complex number c, and therefore the image changes with c. We give the value for c by moving the mouse on the screen.
Same controls as the Mandelbrot set, except that moving the mouse on the screen changes the value of c. If you want to fix an image so you can zoom in on a specific point, you press the space bar.
Divide every square into nine smaller squares. Then remove the middle one of those nine. That's the idea behind the Sierpinski carpet. It may look like a disco floor, but it is a fractal in the way that if you zoom in on any part of the carpet, you see the carpet again.
A very similar pattern to the Sierpinski carpet, but generated in a completely different way. I use a chaos game to generate this fractal, and therefore at first the triangle looks different every time I create it. Let it render for a while, though, and you can see the same pattern as the Sierpinski carpet, but then with squares. Pretty cool!
