The Archons are made using a MATLAB code which solves (analytically) two identical point vortices with opposite rotation, colliding.

Each Archon has a different set of vortex coordinates in the x,y plane and the points at which solutions are calculated is varied. Also a colour scheme is chosen.

A selection of my favourites below

clear; clc;
Za=1+1.i; Zb=conj(Za);
xlim=4; step=xlim/95;
z=x+1iy; w=log((z-Za)./(z-Zb))+log((z-Zb)./(z-Za))/(2*pi);
figure(1); clf;
contourf(xlist,xlist,w’); axis square; axis off;

Creates this:

And then they are edited/cropped etc.