This is a video of a program that sorts the pixels of an image over the course of one second (for a nice animation) into different color spaces in response to key presses. The first color space is the RGB Color Cube, the second is the HSV Color "Cube" (due to a misunderstanding, the correct HSV Color Space which is a cylinder is shown below), the third is a 2D color space that I made up which I call a "Color Wheel" (but not the actual color wheel), and the last one is another made up color space, which I call the "Color Fan". Lastly, the pixels travel back to their original location and then I turn it back into the wheel and spin it.
The HSL Color Fan
This is a 2D color space that I created using HSL (Hue, Saturation, Lightness). I made a vector that separated every pixel in the original image into hue, saturation, and light values. Then, I calculated the position for each pixel with the following formula:
x position = hue * cos( saturation / ( light + 1))
y position = hue * sin ( saturation / (light + 1))
z position = 0
because it's a 2D space
Adding one to the denominator is necessary to avoid dividing by zero in some cases.