Published scene snapshots

Welcome. Today we'll explore how a nonlinear complex function warps space — turning an ordinary grid into something beautiful. On the left we have the input complex plane. Every point here is a complex number, z equals x plus i y. The blue lines are horizontal — they keep the imaginary part constant. The teal lines are vertical — they fix the real part. Together they form a perfect rectangular grid. Concentric circles in coral show points equidistant from the origin. Now we apply our function: f of z equals z squared plus 0.35 times z cubed. On the right, every straight line bends and stretches. The grid is no longer uniform — the function pulls and twists it according to the magnitude and angle of each complex number. The concentric circles also deform, fanning out into graceful spiraling arcs. Let's pick one specific point z on the left and watch exactly where f sends it on the right. This is called a conformal map — it preserves angles locally even as it dramatically reshapes the overall geometry.