I Choas and conservation

One needs to distinguish between physical symmetries and mathematical symmetries.

Noether's Thm can be stated informally as:

If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.

I haven't read the Strogatz book, but two questions that come to mind are:

Is the purported symmetry in fractals a continuous symmetry?

Is the purported symmetry in fractals a physical symmetry (really a perfect symmetry in a physical realization)?

A lot of purported symmetries in physical systems are neither exact nor continuous.

 

This is at the edge of my understanding: scale invariance (self similarity) is associated with conformal symmetry:

https://en.wikipedia.org/wiki/Conformal_symmetry

These are typically associated with phase transitions, but I think you can also generate a conserved energy-momentum tensor from this.