Dance, Factors, Dance

A Variation On Yorgey's Factorization Diagrams

by Stephen Von Worley on October 29, 2012

Upon first sight of Brent Yorgey’s brilliant Factorization Diagrams, I knew that I should take his lovely little dots and make them dance.

Our first tango would be inspired by the digital clock, with a separate diagram for each of hours, minutes, and seconds. For example, we’d portray 4:34:27 am like so:

4:34:27 on the Factor Clock

One night, plans discreetly set, we stole away, rendezvoused, and had our fun prancing about. But alas, what the encounter had in grace, it begged for drama. Quite simply, there wasn’t enough panache – dynamic range – because while hours go up to 23, and minutes and seconds to 59 (*), the diagrams don’t really start cooking until they reach the triple digits. And, per the choreography, zero maps to a motionless blank space, or, if represented by an alternate step, a stray left foot in a square clog, staggering unnaturally amongst the positive, round-slippered wholes.

So, instead, we practiced the best parts of our “clock” routine – the rhythmic movements and snappy transitions – and distilled the remainder to its essence.

Factorization Diagram: 729

And thus was born the Factor Conga: a promenade of primes, composites, and their constituents, arranged with an aesthetically-tuned variation of Yorgey’s rules, one per second.

Please play with the interactive, and do give it a minute to hit its stride. Or whirl there with a tap or two of the fast forward button.

This is what the dance clubs look like on Alpha Centauri.

For various reasons, the original animation topped out at 10,000. Use the unlimited version to enter the device-wedging, battery-burning beyond!

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