Schwarz performs two successive Schwarz-Christoffel transformations of the complex plane: f(z)=1+(zz0)/(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 the mouse. 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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Applets Gallery / Schwarz / created Sunday, 5 July 1998
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Copyright © Greg Egan, 1998. All rights reserved.