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Author Topic: Basic location & zoom question  (Read 1649 times)
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jwm-art
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« on: January 04, 2010, 09:04:31 PM »

A basic question, which seems to get complicated!

I have three test programs, Xaos, Fraqtive, and GnoFract4d. Four including my own, but that is why I'm asking.

I have zoomed into the largest mini-brot where y = 0, so that it almost fills the view (the characteristics it shares with the main M-Set, that is).

Next I set x = -1.77. In both Xaos and Fraqtive the minbrot remains within the view, but in GnoFract4d, it does not.

In Xaos, I set the 'radius' (controls zoom) to 0.064, and in GnoFract4d 'size' (controls zoom;-) to 0.064.
Despite the actual drawing area where the images are displayed in both programs carefully being set to both the same size, the sizes of the minibrot differ (aswell as x being offset differently in GnoFract4d).

Then we come to Fraqtive, where the zoom factor can only be entered in the form of 10^1.24 - a value which gives a very similar result to Xaos with radius set to 0.064.

So what is the standard way here?

My program internally uses three variables for this, xmin, xmax, and ymax - no zoom variable, and I would like the GUI to be able to translate this for the user into an x, y, and zoom amount, but I need something I can be sure of!

So when I go to a deep-zoom video on youtube for example and it says it zooms to such and such a depth, I want to be able to compare the depths I zoom in my program to these, and for the figures to be reliable.

What is the standard zoom value of an image for example, the default image that appears when you start Fractint (which reminds me, I can still test that also :-)

What _IS_ the standard?
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David Makin
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« Reply #1 on: January 04, 2010, 10:15:17 PM »

It's a while since I used Fractint, but I believe that's the magnification method/standard followed in Ultra Fractal, ChaosPro and I think Fractal Explorer and others too.
The default magnification is 1.0 and a 4*3 display window has a horizontal width of 4 (real) and  a vertical width of 3 (imag) at magnification 1 - for instance I think in all the above programs the default Mandelbrot view goes from top-left (-2.5,1.5) to bottom right (1.5,-1.5) with the centre (-0.5,0) and magnification 1.0 so magnification 4 at the same location goes from (-1,0.375) to (0,-0.375).
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cKleinhuis
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« Reply #2 on: January 04, 2010, 11:12:08 PM »

i think it is a simple precision problem, you said you are using your own program, so, what you most certainly see is the end of your number system ( float, double ) those
programs usually implement their own floating point methods with arbitrary precision  :smiley angel police afro
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jwm-art
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« Reply #3 on: January 04, 2010, 11:32:47 PM »

i think it is a simple precision problem, you said you are using your own program, so, what you most certainly see is the end of your number system ( float, double ) those
programs usually implement their own floating point methods with arbitrary precision  :smiley angel police afro

I'm talking about the reference point for zoom values and coordinates. The programs I've tested, where they have two coordinates for x,y, what are these in reference to? The middle of the window, the top left of the window, etc? As I explained, there seemed to be differences. This does not have anything to do with whether I am using arbitrary maths (I am when long double precision runs out) or not. What does a zoom value of 1.0 mean, without a reference to something else? This is something I've put off tackling for a long time, so it's taking me a few takes to get what I mean across :-)

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jwm-art
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« Reply #4 on: January 04, 2010, 11:42:50 PM »

It's a while since I used Fractint, but I believe that's the magnification method/standard followed in Ultra Fractal, ChaosPro and I think Fractal Explorer and others too.
The default magnification is 1.0 and a 4*3 display window has a horizontal width of 4 (real) and  a vertical width of 3 (imag) at magnification 1 - for instance I think in all the above programs the default Mandelbrot view goes from top-left (-2.5,1.5) to bottom right (1.5,-1.5) with the centre (-0.5,0) and magnification 1.0 so magnification 4 at the same location goes from (-1,0.375) to (0,-0.375).

Thanks, that does makes some kind of sense. So it seems it is still down to a choice made at some point - without a display,  there is no reference point, nothing which says how much magnification there is or is not - unlike say a geographical map? Is this making sense?

« Last Edit: January 04, 2010, 11:45:23 PM by jwm-art » Logged
cKleinhuis
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« Reply #5 on: January 05, 2010, 02:13:52 AM »

ok, missed it, daves explanaition is good,

the advance when working with a point and scale method is for easier control of rotation in my eyes cheesy
and translating and similar stuff is getting quite expansive

but it also has to be said, that the point usage is just a view of the data, most fractal programms allow both
methods simultaneously, e.g. ultrafractal, when you change one, the other also changes

 angel

i think it is a simple precision problem, you said you are using your own program, so, what you most certainly see is the end of your number system ( float, double ) those
programs usually implement their own floating point methods with arbitrary precision  :smiley angel police afro

I'm talking about the reference point for zoom values and coordinates. The programs I've tested, where they have two coordinates for x,y, what are these in reference to? The middle of the window, the top left of the window, etc? As I explained, there seemed to be differences. This does not have anything to do with whether I am using arbitrary maths (I am when long double precision runs out) or not. What does a zoom value of 1.0 mean, without a reference to something else? This is something I've put off tackling for a long time, so it's taking me a few takes to get what I mean across :-)


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Duncan C
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« Reply #6 on: February 21, 2010, 04:43:00 AM »

i think it is a simple precision problem, you said you are using your own program, so, what you most certainly see is the end of your number system ( float, double ) those
programs usually implement their own floating point methods with arbitrary precision  :smiley angel police afro

I'm talking about the reference point for zoom values and coordinates. The programs I've tested, where they have two coordinates for x,y, what are these in reference to? The middle of the window, the top left of the window, etc? As I explained, there seemed to be differences. This does not have anything to do with whether I am using arbitrary maths (I am when long double precision runs out) or not. What does a zoom value of 1.0 mean, without a reference to something else? This is something I've put off tackling for a long time, so it's taking me a few takes to get what I mean across :-)



JWM,

When I first started doing this, I used min and max real and imaginary values. I found that cumbersome. Too many numbers to juggle if you want to adjust the magnification and keep the same center (a very common thing to do.)

I switched to using the center point of a plot, and a magnification value. Using the center of the plot is much more useful than using one of the corners. If you use the center, you can change the zoom level and the plot zooms in/out smoothly on the same center point.

For my app, I use the "real width" of the plot, or max_real - min_real. Thus, the smaller the real width, the higher the magnification. I've seen quite a few apps that use this same approach.

David's explanation of the zoom level used by FractInt/Ultrafractal makes good sense. It should be easy to write a conversion between that method and the "real width" method I use. I'm too tired to think about it right now. I guess it would be ideal to allow users to input the zoom level using either method.


Regards,

Duncan C
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Regards,

Duncan C
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