CODEWITHSUNDEEP
matlab
rosorosoo
rosorosoo

Reputation: 15

How to create this particular fractal pattern in MATLAB?

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

Upvotes: 1

Views: 151

Answers (1)

HansHirse
HansHirse

Reputation: 18925

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:

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 = 15

Output for d = 99:

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.

Upvotes: 1

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