Why do the plot and patch commands both not execute in Matlab? - matlab

Question

So I was tasked with plotting the Golden Rectangles along with the Golden Spiral over top of the rectangles. We were given the code for the rectangles, for the "spiral" I used multiple arcs from this forum post, and I can only use if and for statements. The code for the rectangles works and the code for the spiral almost works, but what I really need is to get the patch to display behind the plot. This is the code that I have now:
clear variables; close all; clc
phi = (1+sqrt(5))/2;
x0 = 0;
y0 = 0;
for i = 1:8
edgeLength = 1/(phi^(i-1));
moveLength = 1/(phi^i);
modStep = mod(i,4);
if (modStep == 1) %move W, orient NW
x0 = x0 - moveLength;
sx = [x0 x0 x0-edgeLength x0-edgeLength];
sy = [y0 y0+edgeLength y0+edgeLength y0];
%spiral
P1 = [(x0-edgeLength);y0];
P2 = [x0;(y0+edgeLength)];
P0 = [x0;y0];
n = 1000;
v1 = P1-P0;
v2 = P2-P0;
c = det([v1,v2]);
a = linspace(0,atan2(abs(c),dot(v1,v2)),n);
v3 = [0,-c;c,0]*v1;
v = v1*cos(a)+((norm(v1)/norm(v3))*v3)*sin(a);
if i == 1
vx1 = v(1,:);
vy1 = v(2,:);
elseif i == 5
vx6 = (v(1,:)+(1/(phi^5)));
vy6 = (v(2,:)+(1/(phi^5)));
end
end
if (modStep == 2) %move N, orient NE
y0 = y0 + moveLength;
sx = [x0 x0+edgeLength x0+edgeLength x0];
sy = [y0 y0 y0+edgeLength y0+edgeLength];
%spiral
P1 = [x0;(y0+edgeLength)];
P2 = [(x0+edgeLength);y0];
P0 = [x0;y0];
n = 1000;
v1 = P1-P0;
v2 = P2-P0;
c = det([v1,v2]);
a = linspace(0,atan2(abs(c),dot(v1,v2)),n);
v3 = [0,-c;c,0]*v1;
v = v1*cos(a)+((norm(v1)/norm(v3))*v3)*sin(a);
if i == 2
vx2 = v(1,:);
vy2 = (v(2,:)+(1/(phi^2)));
elseif i == 6
vx5 = (v(1,:)+(1/(phi^5)));
vy5 = (v(2,:)+(1/(phi^6)));
end
end
if (modStep == 3) %move E, orient SE
x0 = x0 + moveLength;
sx = [x0 x0 x0+edgeLength x0+edgeLength];
sy = [y0 y0-edgeLength y0-edgeLength y0];
%spiral
P1 = [(x0+edgeLength);y0];
P2 = [x0;(y0-edgeLength)];
P0 = [x0;y0];
n = 1000;
v1 = P1-P0;
v2 = P2-P0;
c = det([v1,v2]);
a = linspace(0,atan2(abs(c),dot(v1,v2)),n);
v3 = [0,-c;c,0]*v1;
v = v1*cos(a)+((norm(v1)/norm(v3))*v3)*sin(a);
if i == 3
vx3 = (v(1,:)+(1/(phi^3)));
vy3 = (v(2,:)+(1/(phi^2)));
elseif i == 7
vx7 = (v(1,:)+(1/(phi^7)));
vy7 = (v(2,:)+(1/(phi^6)));
end
end
if (modStep == 0) %move S, orient SW
y0 = y0 - moveLength;
sx = [x0 x0-edgeLength x0-edgeLength x0];
sy = [y0 y0 y0-edgeLength y0-edgeLength];
%spiral
P1 = [(x0-edgeLength);y0];
P2 = [x0;(y0-edgeLength)];
P0 = [x0;y0];
n = 1000;
v1 = P1-P0;
v2 = P2-P0;
c = det([v1,v2]);
a = linspace(0,atan2(abs(c),dot(v1,v2)),n);
v3 = [0,-c;c,0]*v1;
v = v1*cos(a)+((norm(v1)/norm(v3))*v3)*sin(a);
if i == 4
vx4 = (v(1,:)+(1/(phi^3)));
vy4 = (v(2,:)+(1/(phi^3)));
elseif i == 8
vx8 = (v(1,:)+(1/(phi^7)));
vy8 = (v(2,:)+(1/(phi^7)));
end
end
end
patch(sx,sy,0.8+0.2*rand(1,3));
vx = [vx1 vx2 vx3 vx4 vx5 vx6 vx7 vx8];
vy = [vy1 vy2 vy3 vy4 vy5 vy6 vy7 vy8];
plot(vx,vy);
axis equal
In the code, the comments about North, West, etc. are in reference to the rectangles that are displayed and their orientation. The parts of the code that make up the spiral are likewise labeled.
So I really have two questions, however, the one that is most pressing is why will only the plot(vx,vy) command only work and not the patch? I tried looking at other examples of things but they seem to just type each command in in the order they want them to print and it does it.
The other issue I have it that when I do run this code the arcs work perfectly for i = 1:4 but after that, you can see, the lines are all messed up. I don't really know why that is either.
If I left out any other information I'm sorry!
Thank you