New Views of the Divisor Plot

(This post was originally published in October of 2013 in http://ventrellathing.wordpress.com/ I moved it here because this is a better home for it.)

Recently, a fellow number pattern explorer (Gregory Bryant) showed me some patterns he discovered, which he calls Factor Map:

plot

It’s a variation of something I discovered years ago, which I call the Divisor Plot – a special way of seeing composite numbers that reveals some amazing patterns – in particular…parabolas!

Screen Shot 2013-10-09 at 9.47.12 PM

The basic plot had been explored by several people in the past (including Wolfram), but until recently, only small numbers were plotted.

new_Wolfram

Gregory found a way to create the pattern out of parabolas only. He plots the odd-numbered parabolas as red and the even-numbered ones as blue. (His plot is also rotated by 90 degrees)…

image6

Robert Wannamaker has applied similar ideas to musical polyrhythms:

polyrhythms

I discuss these patterns more fully in my blog post, “Barking up the Prime Number Tree“:

div_plot

I believe that we number pattern explorers are contributing to a new revolution in mathematics – a way of understanding very large numbers which behave more like physical models of the universe than they do traditional math.

This revolution in math is also visually stimulating.

spiral

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