This is a demo of an idealistic model of Geiger counter clicking, with deltaTime adjustment. The code takes two constants: the background clicks-per-minute (CPM), and the CPM from the source (the red dot in the center) at 1 meter away. (For this demo, 1 meter = 30px on the screen, as represented by the blue grid.) The sliders here deal in CPM, but the internal variables deal in clicks-per-milisecond (CPMS), which is just CPM / 60000. To determine the probability of at least click occuring over a time frame t at a distance d from the source (with source CPMS s and background CPMS b), this equation is used: 1 - exp(-t * (b + s/d^2)). Derivation: Let's approximate radiation and a Geiger counter like this: we construct a sphere of radius d (the distance of the counter from the source) and pick a random point on the sphere. The Geiger counter is an area on the surface, whose area is constant with distance. So, the chance of the point hitting the Geiger counter is g / 4pi * d^2. We can change this to s / d^2, where s is the probability of a hit at distance 1. (This is the inverse-square law and also applies to visible light and sound, by the way!) However, this breaks down as we get close to the source. So, we should try firing lots of rays at a proportionally-small Geiger counter. To get the probability that any one of these rays hits the counter, we can use the formula for "or", which is 1 - (1 - p)^n. Taking the limit of this as n goes to infinity, we get 1 - exp(-p). How do we add deltaTime to the mix? I'm sure there's a nicer explanation, but the way I found it was to use the "or" formula again, with n being deltaTime. 1 - (1 - (1 - exp(...)))^n simplifies to 1 - exp(n * ...), so our formula becomes 1 - exp(-ts/d^2)). Adding the probability that each "individual" hit is due to background radiation, we get the final formula of 1 - exp(-t * (b + s/d^2)). To get the expected CPM, we just use the inner part of the equation, with t = 60000 (since there are 60000 milliseconds in a minute.) So, the expected CPM is 60000 * (b + s/d^2)). The clicking sound is from here: https://freesound.org/people/parabolix/sounds/417424/
