Jack-o'-Lantern: Light Through Carved Walls (2D cross-section)

This simulator visualizes a top-down slice through a jack-o'-lantern's wall as a ring whose local thickness you can carve away by dragging directly on it. Every point on the ring computes its own candlelight transmittance from the real Beer-Lambert attenuation law, T = e^-μd, so thinner carved regions glow exponentially brighter, not just proportionally brighter. A scattering-softness control blends in a small neighbourhood average of thickness before the exponential is applied, reproducing how real translucent flesh scatters light sideways and softens a sharp carved edge into a warm halo.