MHB Is a fractal always a predictable pattern?

[OMGMathPLS]

It never goes crazy and starts doing it's own unpredictable number pattern or sequence, right? Thanks in advance.

 

[zzephod]

It never goes crazy and starts doing it's own unpredictable number pattern or sequence, right? Thanks in advance.

Coastlines are often considered fractal, in fact they are one of the earliest known structures to be considered fractal and they are not deterministic. Same with fractal landscaped used in CGI (pseudo-non-deterministic).

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[OMGMathPLS]

Coastlines are often considered fractal, in fact they are one of the earliest known structures to be considered fractal and they are not deterministic. Same with fractal landscaped used in CGI (pseudo-non-deterministic).

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Can a fractal be irrational and non repeating?

 

[Nono713]

Can a fractal be irrational and non repeating?

Strictly speaking a fractal is any structure which exhibits self-similarly at any scale. So in some sense it kind of has to have a periodic component. But it can still be quite rich in features. For instance, take a look at the Mandelbrot fractal, if you zoom in on it at various levels of detail you tend to see more and more elaborate patterns, but ultimately they are just the same few types of symmetry repeated over and over again in slightly different ways.

 

[I like Serena]

For instance, take a look at the Mandelbrot fractal, if you zoom in on it at various levels of detail you tend to see more and more elaborate patterns, but ultimately they are just the same few types of symmetry repeated over and over again in slightly different ways.

Interestingly, I believe that the Mandelbrot fractal does not repeat.
Except for its symmetry, its shape is really different everywhere.
It's kind of fun to zoom in somewhere, and discover that it does not show the repeatable pattern that you would sort of expect.

 

[zzephod]

Strictly speaking a fractal is any structure which exhibits self-similarly at any scale. So in some sense it kind of has to have a periodic component. But it can still be quite rich in features. For instance, take a look at the Mandelbrot fractal, if you zoom in on it at various levels of detail you tend to see more and more elaborate patterns, but ultimately they are just the same few types of symmetry repeated over and over again in slightly different ways.

Fractal is a structure where its Hausdorff dimension (strictly) exceeds its topological dimension.

See here

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