Ulam spiral,prime spiral
clc; clear all; close all; sz = 201; mat = spiral(sz); pm = ~isprime(mat); figure('Position',[0 0 800 800]); imagesc(pm); colormap bone; caxis([0, 1]);axis off;
Prime factor colormap
Black dots are prime numbers. As lighter is the dot as higher is the number of prime factors of that number in the Ulam spiral.
sz = 201; mat = spiral(sz); matf = zeros(sz); for i = 1:sz for j = 1:sz fac = factor(mat(i,j)); fm = size(fac); matf(i,j) = fm(2); end end figure('Position',[0 0 800 800]); imagesc(matf); colormap hot; caxis([1, max(matf(:))]);axis off;
Ulam spiral of prime number of prime factors
Black dots corespondend to the numbers in Ulam spiral which has a prime number of prime factors.
sz = 201; mat = spiral(sz); matf = zeros(sz); for i = 1:sz for j = 1:sz fac = factor(mat(i,j)); fm = size(fac); matf(i,j) = fm(2); end end figure('Position',[0 0 800 800]); pm = ~isprime(matf); %sum(pm(:)); imagesc(pm); colormap bone; caxis([0, 1]);axis off;
Small Satellites 