This page combines two visualizations of a class of number sequences that I have been playing with for most of my life. I call them "fibbly sequences". Each sequence is defined by two values: a seed and a modulus. The multi-colored square on the left is called the "equivalence class fractal" and represents relationships among different sequences with the same modulus, while the curves in the background (which appear if you click on the fractal) represent a single sequence.
Click and drag the blue circle on the top slider to adjust the modulus. You may also use the left and right arrow keys to adjust the modulus by an increment of 1. To use a different increment, type it in and then use the "[" or "]" keys.
Click and drag the blue circle on the lower slider to adjust the color map of the fractal.
Click on a square in the fractal to select a seed. Drag your selection outside of the fractal to clear it.
Hit the "H" key to hide everything but the visualizations and the modulus slider. Hit "H" again to reveal the hidden elements.
Hit the "R" key to randomize the modulus and seed at regular intervals. Hit "R" again to stay on the current selection.
For more information about these sequences, their mathematical properties, and the visualizations on this page, see the About page.