Snowball Effect

The "snowball effect" is a metaphor for uncontrolled, exponential growth.

You start with a small snowball and roll it through the snow. The snow sticks to the outside, and the snowball gets bigger and heavier. The added weight causes the ball to compress more snow beneath it and it picks up more snow with each rotation. As its diameter increases, the surface area increases exponentially. Before long, the snowball is too massive to move (on a flat surface) or stop (on a decline).

Exponentially with respect to what? Certainly not its diameter.

pi4r^2... it's exponential with respect to the radius, and hence the diameter (don't confuse exponential with geometric)

You mean don't confuse it with "arithmetic". Geometric and exponential are typically synonyms in this context. Arithmetic means an addition per time step, geometric means a multiplication, and the latter after t time steps is given by O(exp(t))

You're probably right; I was thinking that geometric implies a variable in the exponent wheras exponential merely denoted a variable raised to an exponent.