Pick a scenario; every slider below stays editable.
Sound from each point of the channel (weight 1/r²) arrives after r/c. The first sound is from the bottom of the channel, the last from the cloud end: the length of the rumble is set by the geometry. Dashed lines: first and last arrival.
Press the sweep (two strikes per exponent).
The science
Leader as a growing equipotential. The ionised leader channel conducts, so the whole channel sits at the cloud potential (here phi = 0) while the ground is at phi = 1. Between them the potential obeys Laplace's equation ∇²phi = 0 (solved on the grid by red-black over-relaxation). The leader extends into a neighbouring cell with probability p ~ phieta (Niemeyer, Pietronero and Wiesmann 1984): the field at the tip decides where the discharge goes. With eta = 1 a branched fractal appears; large eta concentrates growth at the strongest tip (a nearly straight channel); eta = 0 ignores the field (compact Eden-like cluster).
Measures. The box-counting dimension D = d ln N(s) / d ln(1/s) of the channel cells (boxes of 2 to 16 cells), the number of channel tips (branch ends) and the tortuosity (main-channel length over the cloud-to-ground distance). On this small grid D is lower than the 1.7 usually quoted for large DBM clusters (finite-size effect); only the trend with eta is robust.
Thunder. The speed of sound is c = 331.3 sqrt(1 + T/273.15) m/s. Light arrives essentially instantly (3 microseconds per km), so the flash-to-bang delay of an observer at ground distance D is D/c (about 2.9 s per km at 20 C). Sound from channel points at height z arrives at sqrt(D² + z²)/c, so the rumble lasts (sqrt(D² + h²) - D)/c for a straight vertical channel of height h.
Honest simplifications. The discharge is a 2D slice with 4-neighbour growth and no stepping physics (real leaders step about 50 m at a time and meet an upward streamer); the ground is a flat perfect conductor so no object attracts the strike; no charge distribution inside the cloud; the acoustic model is straight-ray geometric (no shock-wave generation, refraction, wind, absorption or echoes) and uses the flat 2D channel path with a small out-of-plane jitter drawn only for looks. The cloud, trees and mast are scenery. Cloud-base height only rescales metres per cell. Never shelter under trees in a real storm; this is a physics model, not safety advice.