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Iris (Jieun) Kim — home

Projects / Interactive

Generative Art Playground

Mathematics, taken apart and watched. Three small visual systems — a grid bent by a complex mapping, a field of flowing lines, a curve traced from one changing parameter — each exactly what its equation says and nothing more. Part of Mathematics, Perception, and Artistic Expression, the question this page puts a hand to rather than argues.

A grid on the complex plane, and what z², z³ or 1/z does to it.

Streamlines of a two-dimensional vector field, integrated with Runge–Kutta.

Lissajous figures, rose curves and hypotrochoids, traced from one parameter.

A grid on the complex plane, and what z², z³ or 1/z does to it.

z-planew = f(z)
Source grid on the left, f(z) = z² applied to it on the right. A gap in a curve marks a point the mapping sends to infinity or outside this view — never bridged, only broken. No breaks at the current settings.
Mapping
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f(z) = z² and f(z) = z³ are finite everywhere, so every break on the right comes from the view limit — the mapping genuinely does send some of this grid outside the window shown. f(z) = 1/z is different: it is undefined at z = 0 itself, and grows without bound as z approaches it, so the lines through the origin break there regardless of the view limit.

No compositions here are original mathematical discoveries — every mapping, field and curve is a standard one. What is here is the chance to move its parameters and watch. International Klein Blue, used within each canvas, is a digital approximation of the pigment; this page does not claim to reproduce it exactly.