Basic Matlab Fractal Function (Recursion Loop Help)

I am attempting to create a function that creates a T-patterned fractal by rotating points and drawing lines as the counter increases. However, I cannot get past the first T shape. If I enter in additional branches (3,4 or 5), I simply get increased horizontal lines drawn onto the left branch only. Where has my code gone wrong?

close all; clear all; clc;

% Main 

length = 1;
ratio = .5;
branches = 2;
theta = 90*pi/180;

xold =0;
yold =0;
index =1;
while index<=branches
    if index==1

xnew =length*cos(theta);

ynew =length*sin(theta);

   figure(1); hold on;
          axis ([-1,1, -1,1])
  line([xold, xnew],[yold, ynew])
      else
          % Draw Left
          T = [cos(theta), sin(theta); -sin(theta),cos(theta)];

          x =length*cos(theta);
          y =length*sin(theta);
          temp = T'*[x;y];
          xnew = temp(1,1);
          ynew = temp(2,1);
          figure(1); hold on;
          axis ([-1,1, -1,1])
          line([xold, xold+xnew],[yold, yold+ynew])
          % Draw Right
          line([xold, xold-xnew],[yold, yold-ynew])

      end

% figure(1); hold on;
% axis equal
% line([xold, xnew],[yold, ynew])
% line([xold, xnew],[yold, ynew])

length = length*ratio;
xold = xnew+xold;
yold = ynew+yold;

index = index+1;
end

Answer 1

[Walter Roberson]

It is not possible to code a recursive routine in MATLAB without using the "function" statement to name the routine. By definition, recursive code calls itself.

You might perhaps have converted a recursive routine to iterative; if so then it is no longer recursive.

[Ted]

Would I set the "draw left" code to be its own function or can I accomplish the entire fractal through one script?

[Walter Roberson]

My guess is that the fractal could be done with one script, but it would not be a recursive script. For recursion it would have to be a function rather than a script (I shudder at thought of recursive scripts.)

[Geoff]

You can do recursion without function calls, but it's ugly and involves implementing your own stack. Why would you do that? That's what functions are for =)

Answer 2

[Geoff]

So the whole point of using recursion for a fractal is that you call a single function which draws your fractal. Repeated recursive calls are there to draw a smaller version of the fractal in a new location.

I don't know what you want your fractal shape to look like, but you should start with this underlying approach. Also I think you should take 'figure(1); hold on;' out of the loop and do it only once.

So what minimum parameters are required to draw your fractal?

Well:

length
ratio
branches
theta
xold
yold

I don't know about index. Let's use these to start.

Now some of these control the shape of the fractal (ratio, branches, theta) and others control the size and position (length, xold, yold).

I'm gonna take branches out and assume 2. Because I can't see from your code how you would deal with more than 2. But that'll be obvious in a bit.

So you now have an empty function that draws your fractal:

function DrawFractalT( pos, length, ratio, theta, maxIter )

Note the maxIter which controls the recursion limit. Every time you make a recursive call, you'll reduce this by 1. At the top of your function you need this:

    maxIter = maxIter - 1;
    if maxIter < 0
        return;
    end

The first thing to do is draw the stalk, using your transformation matrix to rotate a vector that describes your stalk, and offset it by the root position.

    % Draw stalk
    T = [cos(theta), -sin(theta); sin(theta), cos(theta)];
    nextpos = pos(:) + T * [0;length];
    line( [pos(1) nextpos(1)], [pos(2) nextpos(2)] );

Actually, that's probably all you need to do. Cos each branch of your fractal is a new 'root' with a different angle. This is what I think you're doing anyway.

    % Draw branches
    dtheta = pi / 2;
    DrawFractalT( ??? );  % left
    DrawFractalT( ??? );  % right

You work out what goes in place of the ???. =)

And you're done.

end

Invoke like this:

length = 1;
ratio = 0.5;
theta = 0;
maxIter = 10;

f = figure;
hold on;
DrawFractalT( [0 0], length, ratio, theta, maxIter );
hold off;