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Daily Fractal & GIFs...
I have several of this type of fractal, but this morning my brain isn't accepting that it's a true fractal even though I captured it off of a fractal site many years ago. What do you think? Is it a true fractal to you?
5 comments:
It's interesting. I didn't know fractals had a definition. Enlighten us, Rick.
I kind of agree with you. Doesn't seem like a true fractal - not in comparison, anyway.
uptonking - In mathematics, a fractal is a subset of Euclidean space with a fractal dimension that strictly exceeds its topological dimension. Fractals appear the same at different scales, as illustrated in successive magnifications of the Mandelbrot set.[1][2][3][4] Fractals often exhibit similar patterns at increasingly smaller scales, a property called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge,[5] it is called affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. - Source: Wikipedia
It looks fractal-ish, but it doesn't seem to have the infinite detail that I expect in a fractal pattern (i.e. as you zoom in, you see more and more detail).
But then I has second thoughts, considering the Mandelbrot set, the fractal that I'm most familiar with.
In a Mandelbrot pattern, you see bands of colors that keep getting more and more detailed as you get closer and closer to the Mandelbrot set (I won’t get into the mathematical definition, but it’s the set of points, infinitely complicated, that are traditionally colored black). Each colored band is “outside” the Mandelbrot set. But what happens if you zoom into one of the colored bands (let’s say it’s yellow)? You would not see infinite detail; you would just see more and more yellow, until the whole field of view is yellow.
So what’s my point? In a Mandelbrot pattern, areas that contain a part of the Mandelbrot set have infinite detail; areas outside the set may have several colored bands, but they have finite detail.
So, possibly this fractal pattern has some areas of infinite detail, and other areas of finite detail, and maybe we’re looking at one of the areas of finite detail.
-Larry
Larry - I'm familiar with the Mandelbrot set but wasn't aware of the finite and the infinite differentiation. Thank you for the explanation.
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