Mathematicians Crack a Fractal Conjecture on Chaos
3 comments
·December 10, 2025mojomark
"Take a chilly window sheeting over with ice: even one oddly shaped snowflake can exert an influence on the final frosty pattern."
I wish writers would do a better job of conveying chaos. Yes, the butterfly flapping it's wings in Brazil (or whatever) can drastically influence the weather a continent away. But I think the true wonder of chaos needs to consider that if that butterfly were turned a few degrees in another direction, the resultant weather can be completely different. It's these infinitesmally small changes in parameters resulting in widely different outcomes that really brings the idea of chaos to life I think.
Nevermark
> Yes, the butterfly flapping it's wings in Brazil (or whatever) can drastically influence the weather a continent away.
> But I think the true wonder of chaos needs to consider that if that butterfly were turned a few degrees in another direction, the resultant weather can be completely different.
The former is simply a different way of saying the latter.
For balance it’s worth say that chaos can greatly magnify the impact of small variables, while greatly suppressing the impact of others. Which are two reasons that make specific predictions in chaotic systems difficult or impossible.
The productive response is to look for behaviors of a given chaotic system. Which can provide a lot of insight, despite specific unpredictability. (I.e. “this heat is going to generate more storms, even if we can’t place those storms on a calendar.”)
In recursive systems, later-emerging stable structures act as constraints that shape the space of earlier and future causal paths, creating the appearance that effects influence causes without violating forward time.