MATLAB: I am trying to make a golden spiral where I input n So far this is my co

Question

MATLAB: I am trying to make a golden spiral where I input n

So far this is my code:

x = 0;

y = 1;

syms v u

axis off

hold on

for n = 1:8

a = fibonacci(n);

% Define squares and arcs

switch mod(n,4)

case 0

y = y - fibonacci(n-2);

x = x - a;

eqnArc = (v-(x+a))^2 + (u-y)^2 == a^2;

case 1

y = y - a;

eqnArc = (v-(x+a))^2 + (u-(y+a))^2 == a^2;

case 2

x = x + fibonacci(n-1);

eqnArc = (v-x)^2 + (u-(y+a))^2 == a^2;

case 3

x = x - fibonacci(n-2);

y = y + fibonacci(n-1);

eqnArc = (v-x)^2 + (u-y)^2 == a^2;

end

% Draw square

pos = [x y a a];

rectangle('Position', pos)

% Add Fibonacci number

xText = (x+x+a)/2;

yText = (y+y+a)/2;

text(xText, yText, num2str(a))

% Draw arc

interval = [x x+a y y+a];

plot(eqnArc, interval, 'b') %used to be fimplicit

end

with a function file:

function result = fibonacci(n)

if (n == 0) || (n == 1)

result=n;

else

result = fibonacci(n-1) + fibonacci(n-2);

end

end

and it outputs this:

Explanation / Answer

CODE :

x = 0;
y = 1;
syms v u

axis off
hold on

for n = 1:8

    a = fibonacci(n);

    % Define squares and arcs
    switch mod(n,4)
        case 0
            y = y - fibonacci(n-2);
            x = x - a;
            eqnArc = (v-(x+a))^2 + (u-y)^2 == a^2;
        case 1
            y = y - a;
            eqnArc = (v-(x+a))^2 + (u-(y+a))^2 == a^2;
        case 2
            x = x + fibonacci(n-1);
            eqnArc = (v-x)^2 + (u-(y+a))^2 == a^2;
        case 3
            x = x - fibonacci(n-2);
            y = y + fibonacci(n-1);
            eqnArc = (v-x)^2 + (u-y)^2 == a^2;
    end

    % Draw square
    pos = [x y a a];
    rectangle('Position', pos)

    % Add Fibonacci number
    xText = (x+x+a)/2;
    yText = (y+y+a)/2;
    text(xText, yText, num2str(a))

    % Draw arc
    interval = [x x+a y y+a];
    fimplicit(eqnArc, interval, 'b')

end

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