The image above contains rows of circles. The number of circles in each row follow the Fibonacci sequence -1. So instead of 1,1,2,3,5,8... it's 0,0,1,2,4,7, and so on.

The pattern is simple. Each circle spawns 2 more circles which are 0.618 the size of the parent and are offset +/- the square root of 0.618 multiplied by the parent's radius.

I sometimes call this the "SSJ Pattern", short for "split split join". This is because every 3rd split also contains a join. For example: the 1st circle splits into 2, those 2 split into 4, which split into 8, but two of the 8 circles (the ones in the center) exist in the same location (they merge). The sequence appears to be 1,2,4,7,12... when in fact it's 1,2,4,8,16... a binary sequence of exponential growth.

Click on the image above to render a large version (width of browser window). You may also specify the number of rows (up to 15). The brighter circles are duplicates (where the pattern merges). The complexity of the algorithm grows pretty fast which is why it's limited to 15 rows.