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my mandelbrot set is defined in a XY world as a rectangular shape,
meaning at any given time i know its most bottom left and upper right corners. is there any way to know what is the total zooming percentage value from the original size by the size of the rectangle?
Thank, igal!

igal k
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2 Answers2

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100*(100% size)/(current size)

This is basic math. If your "100%" box is -2..2 (real), then it has size=4; if your current view is -1..1 then it has size=2, so your zoom % = 100*(base size)/(current size) = 200%.

evil otto
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  • if im not mistaken, your solution can be applied on squares only? – igal k Jan 10 '12 at 21:41
  • Not squares, but yes, just on a single axis, or assuming that you keep the aspect ratio the same. How would you define zoom% with a different aspect ratio Is a box 100x as long but 1/100 as high not zoomed at all? – evil otto Jan 10 '12 at 21:44
  • well that's why i asked the question at first place, on a given box, square-like, finding the zooming ratio is very easy, but when the set is given as a rectangle (3X4) for example, and after few zooming operations the new rectangle is (2X3) how would you define the new ratio? (zoom)? – igal k Jan 10 '12 at 21:48
  • That's just it - you have to choose how to define it. Could be the ratio of the total area displayed, or the ratio of the original to the smallest box with the same aspect ratio containing the viewable area. Pick one, and ask your users if they find that definition useful or confsuing. – evil otto Jan 10 '12 at 21:53
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One useful interpretation of this question is: What (if any) is the common definition of "zoom" when viewing the Mandelbrot set?

So far, I have three examples with three different ways of specifying zoom:

https://mandelbrot.ophir.dev zoom = [pixels per fractal space]

https://mandel.gart.nz zoom = 2 * [pixels per fractal space]

http://mandelset.ru scale = [view height in fractal space] / 2 (smaller is more zoomed in)

>:(

cesoid
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