Focus Area Size <-> Zoom Level

[apeirographer]

Greetings,

In my own programs, I do not use zoom levels, but rather specify the limits of the focus area via floating point numbers.  Is there an established equation for converting between the two?

i.e.: An equation that tells me what zoom level is an area 0.025 points wide (real axis) and 0.010 tall (imaginary axis)?  And vice-versa?

Thank you in advance!

Apeirographer

[quaz0r]

"zoom level" is just a more colloquial terminology for the same thing, and i think is also more often expressed as a positive exponent in this context.  so if the size of a view area was 1e-10, some might say a "zoom level" of 1e10.

[apeirographer]

Shouldn't a focus width/height of 4.00 (-2.00 to 2.00) be zoom level 1 though?  I get the impression that may be the case with the second video (the one I posted).  After all, it starts out zoomed further out than the (-2.00 to 2.00) boundaries, and the initial zoom level is identified as 0.4, then jumps to 1.6 after a bit but not much more zooming.

That suggests to me that the formula is:

Let be magnification.
Let be the width of the focal area.

and

Yielding zoom / width pairs as follows:

1 -> 4
1.01 -> 3.96039604
1.05 -> 3.80952381
1.25 -> 3.2
1.5 -> 2.666666667
2 -> 2
3 -> 1.333333333
4 -> 1
5 -> 0.8
7.5 -> 0.533333333
10 -> 0.4
100 -> 0.04
100000 -> 0.00004
1e+10 -> 4e-10
etc.

This would also explain the "flipping" of the sign.  Does this look right to you, quaz0r?

[quaz0r]

i dont know, i was hoping someone else would chime in.  like you, i dont know what everybody else does, i only know what i do   

[lkmitch]

There's no definitive relation between zoom and width or height (of which I'm aware)--it depends entirely on how a given fractal formula is implemented in a given program.  For example, in Ultra Fractal for the standard Mandelbrot set, a magnification of 1 (= 1*10^0 or zoom level 0?) has a width of 4 units and a height of 3 units, for a 4:3 aspect ratio fractal window.  Change the window aspect ratio to 2:1 and now the width is 6 and height is 3.  Or an aspect ratio of 1:2 gives a width of 4 and a height of 8.

So how you relate height or width to zoom level is up to you.

[Adam Majewski]

https://en.wikibooks.org/wiki/Fractals/Computer_graphic_techniques/2D/plane#Description

HTH