Exponential base $b$: Grid size $n$: Show values:
The grid represents an ecosystem whose population grows exponentially. Use the right and left arrow keys to step forward or backward one time step. As the squares fill up, they turn from green (zero population) to purple (doomsday—maximum population). The population meter at the top gives the current population and the amount of time before doomsday.
Making the grid size larger (looking for more resources) but keeping the growth rate fixed “buys” little extra time. Reducing the growth rate extends the system life more substatially.
In coping (as a society, as a species) with exponential growth (population and resource consumption, for example), we must adjust our intuition to the growth rate and the number of time steps remaining, not to the current “population” relative to the predicted maximum.