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Author Topic: coordinates of deep zooms and multiple precision maths routines  (Read 1974 times)
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jwm-art
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« on: October 26, 2010, 01:16:22 PM »

Ok, is it any use for me to zoom to e100, show you a picture of it, give you the coordinates, and then ask you to confirm with your different fractal program that you find the same image?

For instance in my fractal program I'm using MPFR to get beyond double-precision. MPFR stands for Multiple Precision Floating-point with correct Rounding.

Now, your program on the other hand, might use some other method, perhaps it uses integer maths in some way to emulate multiple precision.

I have often wondered if the correct Rounding of MPFR would make any difference to the accuracy of the plots I'm producing, but have never tested for example using GMP (which MPFR is some kind of extension to IIRC).

Fractals being fractals, I suspect that what amounts to tiny tiny differences of accuracy between different multiple-precision methods will amount to huge differences in the accuracy of coordinates at deep zoom levels (ie e100 and beyond) such that it is impossible for two programs using different methods to produce the same image from the same coordinates.

Any comments?
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jwm-art
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« Reply #1 on: October 26, 2010, 01:19:04 PM »

It must be assumed that both programs are capable of producing the same image for a size of 4.0 and center of 0,0.
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jwm-art
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« Reply #2 on: October 26, 2010, 01:23:55 PM »

Here is such an image to confirm:


Code:
cx -1.99999999913827011875827476290869498831680913663682095950680227271547027727918984035447670553861909622481524128059475119256402014495673143316612650410291078e+00
cy 1.314895443507637575136247566806505002151700520912095709529449343530548994027524594471095886431998077465703233103078489 90793091163454288839050259823313135764e-14
size 2.438973985836665864323936186761775109674131122697142426478857482215339694003819351651898388695357372901540645496273477 4919668813308444965817074271496017899e-107

Alternative coordinate system:
Code:
xmin -1.99999999913827011875827476290869498831680913663682095950680227271547027727918984035447670553861909622481525347546468037589334176463766524204167487475852419
xmax -1.99999999913827011875827476290869498831680913663682095950680227271547027727918984035447670553861909622481522908572482200923469852527579762429057813344729722
ymax 1.31489544350763757513624756680650500215170052091209570952944934353054899402752459447109588643291269271039198285297131114429764671534987862492131309843824072e-14
« Last Edit: October 26, 2010, 01:27:39 PM by jwm-art » Logged
cKleinhuis
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« Reply #3 on: October 26, 2010, 03:57:29 PM »

please use a common color algorithm, to compare images
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jwm-art
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« Reply #4 on: October 26, 2010, 03:59:08 PM »

please use a common color algorithm, to compare images

Yes, agreed, that would be useful. I'm using the bog-standard coloured bands method which is as far as I know, very common  angel
(The palette has alternating colours to bring out the shapes of the bands).
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