In regards to fractals, orbit traps give a new way to render images. As a fractal is created each pixel of the image is calculated by repeating (iterating) a formula over and over. In the case of the Mandelbrot Set the formula is z=z^2+c. As each iteration happens if you follow or plot the path the complex number z takes at each step you can see the “orbit” the point takes.
To see how these orbits behave, open this shader and move your mouse around. The plotted blue lines are the path the iterations for each pixel go through.
The orbit traps themselves are shapes within the complex plane. If the iterating set of points hits this shape then it is “trapped” and the pixel is then colored depending on how close it is to the trap. Not that easy to explain to someone who does not understand the maths involved (and no doubt if you read the above and are not into math then you have a “what the!?” expression now).
Here is the famous Mandelbrot Set.
If the “cross” orbit trap is applied you get an image like the following.
The main centered white cross shape is the main trap. Any time the orbit of a pixel hits within the cross shape it stops iterating and is shaded based on its location within the trap. If only the trap shape is displayed the result is like this image.
There are numerous styles and types of orbit traps out there. Here is another sample of the above Mandelbrot Set rendered with the “stalks” orbit trap.
When you zoom into these orbit trap images you get some more interesting results.
The source code to these orbit traps is included in the Custom Formula Editor of Visions of Chaos. Here are the 5 shaders here for people who want to see how they work.
Mandelbrot Circles Orbit Traps
Mandelbrot Crosses Orbit Traps
Mandelbrot Rings Orbit Traps
Mandelbrot Squares Orbit Traps
Mandelbrot Stalks Orbit Traps
Root-Finding Fractals Orbit Traps
After expanding the root-finding fractals mode in Visions Of Chaos I have now added the ability to render orbit traps within them. The results are as interesting or more interesting than the Mandelbrot orbit trap images. Here are a few example images.
Here is a zoom into the above Newton Fractal using the cross orbit trap and shaded with Perlin Noise.
Even though the movie has a semi 3D appearance of going through a forest of fractal tree trunks the frames are pure 2D. It is the orbit traps that give it the 3D look.
There are many more styles of orbit traps to use and I will no doubt be playing and experimenting with new varieties for years to come.
See for example these shaders.