Kissing Circles

Kissing circles, or osculatory packing (following Pickover’s more relaxed use of the term) is the idea of covering a space with circles that are all tangent to at least on other circle. They are of interest mathematically as a fractal method of covering a space, as well as artistically, providing an interesting background pattern.

Osculatory packing image.

Osculatory packing with scaled color interpretation.

A simple method to generate a packing is to randomly pick a point in space, figure out the shortest distance to another circle, and then place a circle with a radius equal to that distance. (That is, grow the circle to fit.) Continue to repeat this process as long as you want. The more circles you add, the closer you get to filling up the entire space.

Osculatory packing image.

Osculatory packing with rapidly cycling color interpretation.

It can be artistically useful to start with some boundary: a circle, for example.

The library used to generate these images is available on the Internet under a free software license:

OscPacking module on Hackage