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# Yearly Archives: 2014

## 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]);```