Beauty in the Math - Fractals #5

Good morning (locally at least).

More fractals!
I will talk about something else eventually.

Fractal mathematics is not just for making pretty pictures. It also has application in various fields of science as it can be used to describe complex patterns. One example is erosion.

I came across this patterning in some mud.

The fractal below has a very similar appearance. With the right information about soil type and other parameters, a model of how soil erodes could be developed.

Another application is data compression. A relatively simple equation can be used to generate an incredibly complex fractal image. What if you could go in reverse and take a huge multi-Gigabyte satellite map image and compress it into a fractal equation of under 1kB? That's a huge saving on data transfer and storage.
This has been an area of research for a long time.

I am content to make pretty pictures however lol.

Joke of the day... (why not?)

A woman is sitting at her husband's funeral. A man leans in and asks, "Mind if I say a word?"
"No, go right ahead," the woman replies.
The man stands, clears his throat, says, "Plethora", and sits back down.
"Thanks," the woman says, "that means a lot."

Bye.
Richard