Conformal Mappings
Playing around with complex numbers

A conformal transformation is a kind of function defined over all complex numbers that has the basic property of being differentiable, i.e. continuous and smoothly varying. Such a function defines a transformation on the plane that has the property of conserving the angles. This implies that on a very small scale shape is preserved in such a transformation.

Almost all these images are done with a Gimp plug-in called Mathmap. Then it is just a matter of finding an interesting transformation.

For a basic overview and some examples, there is the Mathworld page. For a whole lot of explorations, visit John Matthews page.
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