# How to ensure values stay within range?

e.g. water in a height map

Choosing a range with a margin of error for typical model behaviour seems practical. Could we instead (1). predict maximum values; or (2). have a natural maximum?

1. predict maximum The total energy in a system probably limits the maximum possible values (i.e. if it was all concentrated into one single value). For example, a ring of waves moving towards a center (opposite of ripples on a puddle) would superpose at the center, summing their heights.

Or, for a lower limit, could we calculate the directions of waves and their energy, and find the maximum possible collisions (or are there no known tricks to shortcut its computational complexity)? Or even, predict the actual collisions?

2. natural maximum The speed of light is a natural limit; as you approach it, the same force produces less acceleration. Relativity is a consistent system for nature - so relativistic fluid dynamics should be too. We could choose a different maximum speed, perhaps walking pace. This doesn't seem useful for modelling real systems, but it would limit the range of values in a "natural" way.

(Perhaps $$c$$ is a way to avoid instability in the simulation we inhabit).

• When you refer to a margin of error, are you thinking about an absolute or a relative margin of error? And is the margin of error local or global? – Ertxiem - reinstate Monica Oct 21 '19 at 9:53
• @Ertxiem absolute and global. As if the data type storing the values had a limited range. e.g. a height map modelling waves on a beach, expect them to be less than 1km high. – hyperpallium Oct 21 '19 at 12:00