### Jean-Francois Colonna - Number Theory

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#### Alef

• Posts: 69
• catalisator of fractals

#### Jean-Francois Colonna - Number Theory

« on: September 21, 2018, 05:08:19 PM »
Maybe it is not the best place to post this. There could be some existing thread were it could fit.

Jean-Francois Colonna - Number Theory
gallery

https://imaginary.org/gallery/jean-francois-colonna-number-theory

This is nice:

The additive persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-.

Starting from the origin of the coordinates (at the center of the picture), one follows a square spiral-like path and numbers each integer point encountered (1, 2, 3,…).

Then one displays the N-th point with the false color f(PA(N,B)) where:

PA(N,B) = the additive persistence of N for the base B,
f(...)  = an arbitrary ascending function

Let’s define PA(N,B) with an obvious example:

B = 10
N = 856 (= 8xB^2 + 5xB^1 + 6xB^0)

Then the following sequence is computed:

856 ---> (8+5+6) = 19 ---> (1+9) = 10 ---> (1+0) = 1

It takes three (3) steps to reach a one digit number. Then:

PA(856,10) = 3

and

The multiplicative persistence of the 65536 first integer numbers for the bases 2 -lower left- to 17 -upper right-.

The Goldbach conjecture -the Goldbach comet or the Goldbach rainbow- from 6 to 411678.

p.s.
Not fractal https://eyewire.org/

« Last Edit: September 21, 2018, 05:35:24 PM by Alef »
catalisator of fractals

• 3f
• Posts: 2101

#### Re: Jean-Francois Colonna - Number Theory

« Reply #1 on: September 21, 2018, 08:34:27 PM »
Interesting.

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