These are Fragment shaders I’ve made using webgl. A fragment shader is a program that computes the color for a pixel on the screen. Your GPU can run this program in parallel for every pixel on the screen, so it runs very fast despite there being a lot of pixels on the screen. This is perfect for something like visualizing the mandelbrot set, where each pixel is colored based on where it ends up in the complex plane after performing some computation.
Instead of coloring each pixel discretely based on the iteration count upon escape, This shader uses a continuous coloring which takes into account the iteration count as well as the modulus of the final value. Since it’s colored continuously, it can have some very pretty colors.
Zoom by scrolling and pan the camera by clicking and dragging
This shader uses the same coloring method as the Mandelbrot set shader, but you can select the c-value used to generate the julia set by clicking/dragging the mouse on the screen. You can also zoom in and out with the mouse wheel. If you want to pan the camera, you can do so by holding the mouse wheel down and moving the mouse.
The fractal is generated from simulating a magnetic pendulum swinging over a table with three magnets on it. Each pixel is colored based on which magnet it ends up at and darkened based on how long it took to stop at a magnet. The three magnets oscillate radially from the center to create an interesting visual effect. You can adjust all of the parameters of the simulation to change how it looks and moves.
You can move around by clicking and dragging and zoom in and out by scrolling.
This one is really heavy on the GPU. If it runs too slowly, try decreasing the maximum iterations or making your browser-window smaller.