Pass an image through a registry function and watch what its geometry does to pixels.
f(z) = z + a₂z² + a₃z³ + ….
The lab turns that single coefficient sequence aₙ into an image operator and applies it to a photo, so you can see - not just prove - what each function's geometry does:
its coefficients become a directional convolution kernel (sharpen / smooth / edge), or the function itself is used as a conformal warp w = f(z) of the image disk.
For each run you get the visual output, a distortion map versus the original, the coefficient sequence, the kernel's frequency response, and standard full-reference image-quality metrics
(PSNR, SSIM - Wang 2004, GMSD - Xue 2014).
The subordinating entries are the Ma–Minda φ-functions from Prof. Asha's program (cardioid, sine, nephroid-type, exp-cardioid, quartic) - the same classes whose coefficient bounds are certified on the Proofs page.
We use first-party site metrics to improve navigation: page visits, internal clicks, search result counts (not search terms), and approximate active time. A random tab ID groups events for seven days; GPC/DNT turns this off. The separate visitor count uses a self-hosted pseudonymous fingerprint and also respects GPC/DNT.