Polar warp reinterprets Cartesian coordinates as (radius, angle), turning stripes into rings and scrolling into rotation

Reinterpreting (x, y) as (radius, angle) via atan2 and length transforms an entire image in a single coordinate change. Straight horizontal stripes become concentric rings. Vertical stripes become radial spokes. Scrolling (translating x) becomes rotation. This is the single most useful coordinate change for organic and psychedelic looks in shader-based visuals, and it is cheap — just two or three math ops. The result is a different topology of the same content: global spatial structure flips from grid to polar without changing the underlying function.

Examples

sin((st.x)10.0) produces stripes. After polar conversion (r=length(st), a=atan2(st.y,st.x)), sin(a10.0) produces spokes and sin(r*10.0) produces rings.

Assessment

Describe what happens to a striped pattern when it is viewed through a polar coordinate mapping, and name two visual effects that become trivial after the conversion.