A Portrait of the Root of Sin

on 13 Oct 2021

% See Cleve's post here for more info:

% https://blogs.mathworks.com/cleve/2020/04/15/champagne-portraits-of-complex-functions/

F=@(z) sqrt(sin(z));

axis equal off

m=256;

cm1=parula(m);

cm=[cm1;flipud(cm1)];

n=25;

[x,y]=meshgrid(-1:2/(n-1):1);

c=exp((0:32)/16*pi*1i)/n;

w=F(x+y*1i);

r=abs(w);

th=angle(w)+pi;

sc=20;

for k=1:n

for j=1:n

t=m*th(k,j)/pi/sc;

ix=ceil(sc*t+realmin);

q=cm(ix,:);

p=w(k,j)+r(k,j)*c;

patch(real(p),imag(p),q)

end