Need help with fractal tree plot.

Hi all,

I'm working on a project right now that requires me to construct a function that takes 5 inputs (x1,y1,x2,y2,r) and returns a plot of a fractal tree. The inputs correspond to the endpoints of the "trunk" and r is the number of recursions you wish the function to execute.

For each level drawn two new branches should be drawn at a 90 degree angle from each previous branch. For example, for r=1, two new branches (a left branch and a right branch) would be drawn from the point (x2,y2).

Here is what I have so far (be aware that it is very incomplete):

%To run this file in the command window, call the function fractal_tree1 %and input the appropriate arguments. This function takes input arguments %of staring enpoint and final endpoint of the first branch and the number %levels you wish to be iin your tree.

function recursions = fractal_tree1(x1, y1, x2, y2,r) theta = pi/2; endpoint1 = [x1; y1]; endpoint2 = [x2; y2]; recursions = zeros(2); plot([x1 x2],[y1 y2]) %Draws the initial line that will be the "trunk". hold on

if r > 0 function right_branches = draw_right_branch(x1,y1,x2,y2) theta = pi/2; R_r = [cos(theta) sin(theta);-sin(theta) cos(theta)]; v_12 = [x2-x1;y2-y1]; v_rotated_r = (R_r*v_12)*0.6; endpointnew_r = v_rotated_r+endpoint2; x1 = endpointnew_r(1); y1 = endpointnew_r(2); plot([x2 x1],[y2 y1]) end

    function left_branches = draw_left_branch(x1,y1,x2,y2)
        theta = pi/2;
        R_l = [cos(-theta) sin(-theta);-sin(-theta) cos(-theta)];
        v_rotated_l = (R_l*v_12)*0.6;
        endpointnew_l = v_rotated_l+endpoint2;
        x1 = endpointnew_l(1);
        y1 = endpointnew_l(2);
        plot([x2 x1],[y2 y1])
    end
end

hold off end

If you have any suggestions as to what i can do from here, let me know!

Answer 1

[Iman Ansari]

Hi This works for r=1:

%To run this file in the command window, call the function fractal_tree1 
%and input the appropriate arguments. This function takes input arguments 
%of staring enpoint and final endpoint of the first branch and the number 
%levels you wish to be iin your tree.

function recursions = fractal_tree1(x1, y1, x2, y2,r)
theta = pi/2; 
endpoint1 = [x1; y1];
recursions = zeros(2);
plot([x1 x2],[y1 y2]) %Draws the initial line that will be the "trunk". 
hold on

      if r > 0
          draw_left_branch(x1,y1,x2,y2);
          draw_right_branch(x1,y1,x2,y2);        
      end

hold off 
end

function left_branches = draw_left_branch(x1,y1,x2,y2)
    theta = pi/2;
    R_l = [cos(-theta) sin(-theta);-sin(-theta) cos(-theta)];
    v_12 = [x2-x1;y2-y1];
    v_rotated_l = (R_l*v_12)*0.6;
    endpoint2 = [x2; y2];
    endpointnew_l = v_rotated_l+endpoint2;
    x1 = endpointnew_l(1);
    y1 = endpointnew_l(2);
    plot([x2 x1],[y2 y1])
end

function right_branches = draw_right_branch(x1,y1,x2,y2) 
    theta = pi/2; 
    R_r = [cos(theta) sin(theta);-sin(theta) cos(theta)]; 
    v_12 = [x2-x1;y2-y1]; 
    v_rotated_r = (R_r*v_12)*0.6; 
    endpoint2 = [x2; y2];
    endpointnew_r = v_rotated_r+endpoint2; 
    x1 = endpointnew_r(1); 
    y1 = endpointnew_r(2); 
    plot([x2 x1],[y2 y1]) 
end