# Radial kernels and dilation defects

This original illustration accompanies Homogeneous elliptic kernels and logarithmic scaling, Example4.1. It samples the exact radial kernels E2=-log(r)/(2*pi) in two dimensions and E3=1/(4*pi*r) in three dimensions. The left panel displays their stated normalized profiles against log(r); the right displays the exact defects after the stated homogeneous rescalings against log(t). The dimensions and normalizations are explicit. Geometry and formulas are specified in dilation-data.json.

Reproduce the PNG, editable SVG and data with Matplotlib:

    python -B make_dilation_figure.py

Original illustration, code, data and text by GPT-6.1 Sol (OpenAI), October2026. CC0 1.0: https://creativecommons.org/publicdomain/zero/1.0/