How to create this particular fractal pattern in MATLAB? - matlab

Question

I need to make an array of zeros and ones in this particular fractal pattern:
0 0 0 0 0 1 0 0 0 0 0 0
0 0 1 1 1 1 1 1 1 0 0 0
0 1 0 0 0 1 0 0 0 1 0 0
0 1 0 0 1 1 1 0 0 1 0 0
0 1 0 1 0 1 0 1 0 1 0 0
1 1 1 1 1 1 1 1 1 1 1 1
0 1 0 1 0 1 0 1 0 1 0 0
0 1 0 0 1 1 1 0 0 1 0 0
0 1 0 0 0 1 0 0 0 1 0 0
0 0 1 1 1 1 1 1 1 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0
0 0 0 0 0 1 0 0 0 0 0 0
The actual array should be 100 x 100. The pattern should start from the middle (x,y) coordinate, and expand to look like the pattern (using loops).
So far, I have only managed to make a pattern that looks like a '+' sign. I am not sure how to continue it.
This is my code so far:
n = zeros(16); % using 16x16 array for practice
x = length(n)/2;
y = length(n)/2;
z = length(n) - 1;
xso = length(n)/2; % x axis south movement
xno = length(n)/2; % x axis north movement
yea = length(n)/2; % y axis east movement
ywe = length(n)/2; % y axis west movement
for i = 1:1:z
newyea = move('east', x, yea);
n(x, newyea) = 1;
yea = newyea;
newywe = move('west', x, ywe);
n(x, newywe) = 1;
ywe = newywe;
newxso = move('south', xso, y);
n(newxso, y) = 1;
xso = newxso;
newxno = move('north', xno, y);
n(newxno, y) = 1;
xno = newxno;
end
I also have a user defined function:
function newval = move(dir, x, y)
switch dir
case 'east'
newval = y + 1;
case 'west'
newval = y - 1;
case 'south'
newval = x + 1;
case 'north'
newval = x - 1;
end

Answer 1

Since there were no restrictions given on the appearance of the loop, I would propose the below solution. But, before, let's have a look at your given example:
Either you should restrict the desired dimension d to be odd, i.e. d = 11, 13, 15, ... or you should specify, how the pattern should be continued in case of an even dimension d, like here d = 12. For my solution, I decided to rely on the dimension d to be odd.
Here's the code:
d = 15; % Dimension
A = zeros(d); % Initialize output array A
c = (d + 1) / 2; % Calculate center index (row, column)
A(:, c) = 1; % Add: Cross
A(c, :) = 1;
J = 0; % Auxiliary index
for I = (c+2):2:d % For every second row (or column) from center to border
J = J + 1;
l = 4 * J - 1; % Calculate length of line to draw
s = c - (l-1)/2; % Calculate start point of line
e = c + (l-1)/2; % Calculate end point of line
A(I, s:e) = 1; % Add: "South" line
A(s:e, I) = 1; % Add: "East" line
A(c - 2*J, s:e) = 1; % Add: "North" line
A(s:e, c - 2*J) = 1; % Add: "West" line
end
figure(1); % Show image
imagesc(A);
Output for d = 15 (to compare to given example):
Output for d = 99:
Hope that helps!
If you have some more stricter limitations on the for loop, let me/us know. Then, I will try to modify my code accordingly.