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Fractals don't even need to be self-similar. They just need to have fractal dimension (if you double the size of every feature - the exponent near the scaling f
by ajuc 3y ago
Fractals don't even need to be self-similar. They just need to have fractal dimension (if you double the size of every feature - the exponent near the scaling factor must be non-integer). Self-similarity is the easiest way to make a fractal, but not the only one.
In fact the idea of fractal was invented for real-life non-self-similar objects. The simple self-similar ones are just examples that are easiest to understand.
- ouid 3y agoAs far as i can tell, fractal doesn't have a definition. The closest it ever came was the one you roughly gave.
- idiotsecant 3y agohttps://en.wikipedia.org/wiki/Fractal_dimension https://en.wikipedia.org/wiki/Fractal_dimension Not only are fractals very well defined in mathematical terms, but there are further mathematics based on those definitions.
- ouid 3y agoFrom the article you linked: >Ultimately, the term fractal dimension became the phrase with which Mandelbrot himself became most comfortable with respect to encapsulating the meaning of the word fractal, a term he created. After several iterations over years, Mandelbrot settled on this use of the language: "...to use fractal without a pedantic definition, to use fractal dimension as a generic term applicable to all the variants."
- _a_a_a_ 3y agohttps://html.duckduckgo.com/html?q=fractal%20definition https://html.duckduckgo.com/html?q=fractal%20definition did you even look?
- mfragin 3y agoWhen I was teaching math and comp sci, I used broccoli in an example to explain self-similarity: imagine you're playing with your Barbies or GI Joes and you want to make their dinner plates look like they have real food on them. You can break off a much smaller piece of broccoli and it will look "to scale" on the plate. Try that with a banana! That was to explain the concept of self-similarity, something we CAN see in fractals. Note: for anyone wanting an easy way to experiment with L-systems, there's a built-in feature in Inkscape that is pretty fun to use. It's under "Extensions/Render/L-System"
- dekhn 3y agoI don't perceive broccoli as self-similar at any scale (maybe I'm missing something), but romanesco, for sure. I see at least 3 levels of self-similarity.
- ska 3y ago> maybe I'm missing something I think you are. At the very least, you can clearly break a piece off a floret to resemble a scaled version of the whole head.
- michaelcampbell 3y agoThanks, this and the post to which you replied taught me something that I did not know. TIL...