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It has been quite a while since I've had some introductions to fractal geometry, but only on special cases, e.g., the Sierpinski triangle and other self similar fractals.

Now I have challenged myself to calculate the fractal dimension of the romanesco broccoli, since it has some self similarity. It is illustrated by the images below:

Behold the Romanesco Broccoli in all it's glory!

Side view for more information.

So, my request here is for some references to help me with this goal. If you want to answer with a hint or an important step on this kind problem it is also welcome.

Thanks for the attention and have a good day!

Mark McClure
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    Just a couple of tips on how I'd approach this: (1) Assume the broccoli is the union of copies of itself with linear scale factors $a_1,a_2,a_3,\ldots$. Can you express the dimension as an implicit function of the $a_i$'s? (I think I know the solution to this, but perhaps you want to figure it out yourself.) (2) Suppose the $a_i$'s are in decreasing order (starting from the base of the broccoli head and spiraling in). How does $a_i$ decay as a function of $i$? (Is it exponential? A power law? Something else?) At some stage this will likely entail pulling out a ruler and measuring. :) – tuna Aug 13 '21 at 04:27
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    If you do want a reference for (1) above, look up Moran's Theorem. https://sci-hub.se/https://aip.scitation.org/doi/pdf/10.1063/1.5079401 – tuna Aug 13 '21 at 04:44
  • Thank you very much for the response, I'll try this method. And I did laugh when I read the ruler part. Good day to you! – Fractal Admirer Aug 13 '21 at 06:39

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