There must be a "kick me" sign on my back.
Here's a continuous formula for the fibonacci sequence:
phi = (sqrt(5)+1)/2;
fib(i) = ((phi^i-(-phi)^-i)/sqrt(5)
A good approximation is:
fib(i) = phi^i/sqrt(5)
A quick grad student algorithm of the first image of "nautilus" I find on google would be:
() cls(0);
moveto(xres/2,yres/2);
phi = (sqrt(5)+1)/2;
for(t=1;t<64;t+=.1)
{
r = pow(phi,t/4);
lineto(cos(t)*r+xres/2,sin(t)*r+yres/2);
}
for(t=1;t<64;t+=.25)
{
r0 = pow(phi,t/4);
r1 = pow(phi,(t+PI*2)/4);
for(u=0;u<=1;u+=1/64)
{
r = (r1-r0)*u+r0;
a = (u^2-sqrt(u))/2;
x = cos(t+a)*r+xres/2;
y = sin(t+a)*r+yres/2;
if (u == 0) moveto(x,y);
else lineto(x,y);
}
}
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