Measuring Fractal Dimension ?

[Paul Rubin]

Steven D'Aprano <steve at REMOVE-THIS-cybersource.com.au> writes:
> Depends on how you define "discontinuous". 

The mathematical way, of course.  For any epsilon > 0, etc.

> Catastrophe theory is full of discontinuous changes in state. Animal
> (by which I include human) behaviour often displays discontinuous
> changes.  So does chemistry: one minute the grenade is sitting there,
> stable as can be, the next it's an expanding cloud of gas and metal
> fragments.

If that transition from grenade to gas cloud takes a minute (or even a
femtosecond), it's not a mathematical discontinuity.  The other
examples work out about the same way.