Even starting with one person, it can spread in an instant
Starting with just one infected cell (one person), each turn allows infected cells to infect neighboring healthy cells with a given probability. At first, it may seem to grow slowly, but then you will see it suddenly explode — this is exponential growth.
Why does it look like this? When the number of infected people grows by a constant ratio each turn (doubling, multiplying by 1.5, and so on), the increase is hard to notice at first because the numbers are small. Later, the numbers themselves become large, so the amount of increase becomes larger too. This is a key feature of an exponential function that grows by "multiplying." (You can also see the growth naturally slow down as the graph fills the entire grid.)
Infected: 1Turns elapsed: 0
Infection probability (per neighboring person per turn)25%
💡 On a log scale, the early period of exponential growth appears almost as a straight line. When the graph is a straight line, it means the value is "increasing by a fixed multiple."