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

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: