Schwarz performs two successive Schwarz-Christoffel transformations of the complex plane:
f(z)=1+(z–z0)/(1–z0*z)
which maps z0 to 1 and the unit disk centred on 0 to the unit disk centred on 1, and:
g(z)=(z+1)/(z–1)
which maps 1 to infinity and the unit disk centred on 0 to half the complex plane; z0 is either a random point, or the point where you last clicked on the applet. The pattern displayed is the “pull-back” via the combined transformation of a square tiling of the complex plane, decorated with either a radial or concentric circular pattern.
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