Why are natural patterns rarely geometric (and other curiosities)?

[afternoonspray]

I'm just staring at the cat and his fur has naturally separated into sections. The shape of them reminds me of the shapes made in mud when it dries or the striations in rock - slightly rippled, staggered lines. Then I wondered why this sort of shape often occurs in nature and straight lines and grids don't.

Obviously I have far too much time on my hands today but does anyone know why patterns naturally form like this not in a more orderly shape sequence?

And does anyone else have a weird wondering they want to share and ask about?

afternoonspray Alan Turing - of cryptography fame - did some seminal work in this area many years ago and the implications of his ideas are still being explored.

Thank you so much @OutwiththeOutCrowd. I'm going to look at that right now.

That was magnificent. Thank you. So tragic that he died too young because of bigotry.

Well, sometimes nature does form perfect patterns, look up fractals in nature, some beautiful examples such as snowflakes, leaves, ferns, anenomites.. See also Fibonacci sequence. Did some research into this not long ago and how such patterns can have calming effects on us, very cool stuff

Well you can use maths to model some of the things you are talking about. Some things can't currently be modelled and may in fact be chaotic.
However the mud will be formed by the wind and other external forces. The wind flow will be effected by little variations on the mud surface (as well as things like friction in the boundary layer), which then moves the mud into more variations etc.

A lot of nature does use the Fibonacci sequence. It's fascinating.

I do know a bit about fractals and fibonnacci. I am obsessed with the mathematical beauty of those dahlias that have very tight pompom formations. It was more the repeating of what appears to be less mathematical patterning that intrigued me. Looks random but is it. I'm real;y interested in @Witchend's comment that wind flow would have affected the patterns of mud formation because it's probably wind flow that makes the cat's fur mat in those lovely ribbed tufts. He goes out catting on the local farm and comes back tufty. So ther eis a shape to the wind... God this stuff is so interesting. I wish I were any good at science and could understand it on a more mathematical level.

Wind flow over the top, anything like stones or even roots that effect the mud movement as well as the wind flow.
I did wave motion at university and found it fascinating. I did a whole project on the Gulf Stream and how it alters.

This is such an interesting thread.

@Witchend - how does the Gulf Stream alter and why?

I told DC about the cat's fur having the shape of the wind in it and they were fascinated too. DS1 who studies chemsitry and biology at A level was saying there must be a mathematical formula for the shapes it makes because even though they are irregular they do appear similar so there must be a repeat in some form.

Sorry afternoonspray I did it around 25 years ago and couldn't answer that now.

I seem to remember it isn't totally predictable, however there are ways of predicting likely outcomes. There's also cold patches in the middle of the gulf stream, which appear and disappear.
It was fascinating at the time!

Giant's Causeway is celebrated because the rocks are so unusually geometric...www.iflscience.com/environment/why-columnar-basalt-almost-always-hexagonal/

There was a programme about waves on BBC4 late last night - might be on iPlayer still.

I think there are a lot more regular patterns thsn you might expect. Crystalline forms like the Giant's Causeway, or salt. Plus all the plant and animal examples upthread. Honeycomb. I think that's all more surprising thsn irregular patterns - though I agree they may not be as irregular as they appear to us, and there probably are formulae around it all.

I read somewhere that all patterns in nature follow the principle that the shape of a structure is such because it uses the least amount of energy required to form the structure. There’s a slideshow on bubbles and honeycomb. I’ll find it.

Here:
Link

But that’s ^^ more about perfect geometric patterns obv instead of imperfect ones

@Kiwiinkits - thank you for that. Looks fascinating. I have to go out soom but will look at it this evening.

OP thank you for posting this strangely wonderful question! I've often wondered this. Going to RTFT now.

I know this isn't AIBU but even so you have been totally unreasonable not posting a pic of your moggy

@tellmewhenthespaceshiplandscoz - next time he comes in with wind shapes in his fur I will attempt to get him to pose for me. He's groomed himself today so they aren't there right now.

I'd love to see him!