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Yearly Archives: 2014
Ulam spiral,Prime factors spiral
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;
Henneberg surface, Matlab code
close all; clc;clear all;
[u v] = meshgrid(0:0.1:1); %v = meshgrid(1:0.01:2); i = 1; for u =-pi/2: 0.1:pi/2 j =1; for v = -pi/2:0.1:pi/2 x(i,j) = 2*sinh(u)*cos(v) - 2/3*sinh(3*u)*cos(3*v); y(i,j) = 2*sinh(u)*sin(v) - 2/3*sinh(3*u)*sin(3*v); z(i,j) = 2*cosh(2*u)* cos(2*v); j = j+1; end i = i+1; end surf(y,x,z); axis off;
Ford Circles
clc; close all; fi = 0:0.01:2*pi;
figure('Position',[0 0 500 500]) hold on; for h =1:15 for k = 1:15 R = 1/(2*k^2); x = h/k + R*sin(fi); y = 1/(2*k^2) + R*cos(fi); plot(x,y,'k'); % Symmetric y = -(1/(2*k^2) + R*cos(fi)); plot(x,y,'k'); end end axis([0, 2.2,-1.1, 1.1 ]);axis off;
Dragon Fractal
clc; clear all; close all;
a = ones(1); for i = 1:12 sz = size(a); b = a; ind = ceil(sz(2)/2); b(ind) = ~(b(ind)); sz = size(a); a = [a,1,b]; end st = 1; % Step len = size(a); x0 = 0; y0 = 0; %Initial Lv = 0; % Looking along positive x axis for i = 1:len(2) x1 = x0 - sin(Lv)*st; y1 = y0 + cos(Lv)*st; if a(i) == 1 Lv = Lv + pi/2; else Lv = Lv - pi/2; end xv(i) = x1; yv(i) = y1; x0 = x1; y0 = y1; end
fig = figure('Position',[0 0 800 800]); set(fig, 'color', [0 0 0]); plot(xv,yv,'clipping','off') axis off;
Box Fractals
clc; clear all; close all;
a = 1; figure('Position',[0 0 800 800]) for i = 1 :5 [n m] = size(a); Z = zeros(n,m); a = [a,Z,a; a,a,a; a,Z,a ]; end imagesc(a); colormap bone;axis off; caxis([0, 1]);
clc; clear all; a = 1; figure('Position',[0 0 800 800]) for i = 1 :5 [n m] = size(a); Z= zeros(n,m); a = [Z,a,Z; a,a,a; Z,a,Z ]; end imagesc(a); colormap bone;axis off; caxis([0, 1]);
clc; clear all; a = 1; figure('Position',[0 0 800 800]) for i = 1 :5 [n m] = size(a); Z= zeros(n,m); a = [a,a,a; a,Z,a; a,a,a ]; end imagesc(a); colormap bone;axis off; caxis([0, 1]);
clc; clear all; a = 1; figure('Position',[0 0 800 800]) for i = 1 :5 [n m] = size(a); Z= zeros(n,m); a = [a,Z,a; Z,a,Z; a,Z,a ]; end imagesc(a); colormap bone;axis off; caxis([0, 1]);
clc; clear all; a = 1; figure('Position',[0 0 800 800]) for i = 1 :5 [n m] = size(a); Z= zeros(n,m); if mod(i,2) == 0 a = [Z,a,a; a,a,a; a,a,a ]; else a = [a,a,a; a,Z,a; a,a,a ]; end end imagesc(a); colormap bone;axis off; caxis([0, 1]);
Small Satellites 