Title: Focus Area Size <-> Zoom Level
Post by: apeirographer on May 12, 2016, 03:37:59 AM
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
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
Title: Re: Focus Area Size <-> Zoom Level
Post by: quaz0r on May 12, 2016, 07:59:50 PM
"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.
Title: Re: Focus Area Size <-> Zoom Level
Post by: apeirographer on May 13, 2016, 03:45:07 PM
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?
That suggests to me that the formula is:
Let
Let
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?
Title: Re: Focus Area Size <-> Zoom Level
Post by: quaz0r on May 13, 2016, 06:02:05 PM
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 ;D
Title: Re: Focus Area Size <-> Zoom Level
Post by: lkmitch on May 13, 2016, 06:35:20 PM
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.
So how you relate height or width to zoom level is up to you.
Title: Re: Focus Area Size <-> Zoom Level
Post by: Adam Majewski on May 13, 2016, 09:33:53 PM
https://en.wikibooks.org/wiki/Fractals/Computer_graphic_techniques/2D/plane#Description
HTH
HTH