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Author Topic: buddhabrot in fortran :)  (Read 5967 times)
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Timeroot
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« Reply #15 on: March 11, 2010, 01:43:43 AM »

I found an itneresting website about the mandelbrot discs : http://classes.yale.edu/fractals/MandelSet/MandelCombinatorics/N2Scaling/N2Scaling.html

Shameless plug--I'm the Kerry Mitchell mentioned on that page.  smiley  Michael Frame (who created those class notes) told me about the scaling rule some 20 years ago.  While investigating it numerically (in FORTRAN), I discovered those deviation features.


That's a pretty interesting page. I believe the fractal structure of those plots is somewhat similar tick marks on a ruler. I'm thinking this: if m/n has one value of rtc/rad, then (1/3)+m/6n and (1/3)+m/3n have a similar structure. Also, (1/4)+m/8n and (1/4)+m/4n would also produce similar values. This might explain the compression that occurs off to the side. Indeed, the structure reminds me of the dyadic rationals...

Did you ever try plotting the values, as sorted by n? Or by m? Or maybe a plot (multivalued) where the x-coordinate corresponds to m+n? I would love to see!!!

i'm wondering if it worth it to pre-compute the 3rd and 4th order disc.

i know they are not real disc, and it certainly doesn't worth it to compute a very good estimation, but i can estimate the size of a rough interal disc contained in the 3rd and 4th order disc/shape. It's very cheap in cpu time. (much cheaper than computing the main cardioid, but considering its size : it worth it)


But that would only save any time if you happen to be zooming in on one of those shapes. And in general, a good Mandelbrot pic doesn't have a huge period-3 or 4 mass off to one side...

Has anyone investigated what shapes the bulbs are? When looking at skewed Minibrots, it seems they don't possess any other deformation. I would hypothesize that the bulbs are all exact ellipses (skewed circles), and that there is some correlation between m/n and their skew angle. The angle could be defined as relative to the normal. However, if we defined the angle that way, in order to fully describe the shape one would also need a stretch factor. The alternative would be the skew angle, and the angle relative to the normal, relative to which it was skewed. If someone wrote a program that gathered data on this, and then maybe tried plotting using both of those, I'm sure it would result in some interesting results.
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
Timeroot
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« Reply #16 on: March 12, 2010, 01:49:58 AM »

Ohhhh, I think I understand that plot now. It's just a graph along the surface of the cardioid... I wonder what the ratio would be if you took successively accurate rational approximations of the Fibonacci point. I would still like to see a computation of the skew (if they truly are ellipses) though... and whatever shape they are I wonder if the center - that is, the multiplier - is the actual center of the shape. In the case of an ellipse, I mean the *center*, but of course for more irregular shapes you can define many different points as the center...  afro
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
ker2x
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« Reply #17 on: May 04, 2010, 09:23:20 PM »

I added some easy optimisation to quickly know if a point is in an area of interest or not (more than a few iteration, and not inside the mandelbrot set)
The first one is to choose a "good" random point.
1) There is nothing interesting outside of -1.3 to 1.3 on the imaginary axis
2) There is nothing interesting outside of -2 to 0.5 on the real axis
Code:
c = CMPLX((x*2.5 - 2) ,y*1.3 )


After that, i ignore all point which are in the main cardoid, or in the 2nd bulb.
Code:
IF(((ABS(c - CMPLX(-1,0) )) < 0.25) .OR. ((ABS( 1.0 - SQRT(1-(4*c)) ))  < 1.0 ) ) THEN
     notInMset = .FALSE.
 ELSE
     ....
 END IF

There is probably more optimisation, but thoses ones were easy smiley
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often times... there are other approaches which are kinda crappy until you put them in the context of parallel machines
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ker2x
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« Reply #18 on: May 04, 2010, 11:08:17 PM »

i'm back to good old black and white rendering.
Source code available here : http://github.com/ker2x/Fortran_buddhabrot/blob/BlackAndWhite/buddhabrot.f90

minimum iteration : 10k
maximum iteration : 1 million

Using 3 core in VirtualBox :
real   3m5.918s
user   8m47.050s
sys   0m1.640s



* buddhabrot.png (253.56 KB, 1024x1024 - viewed 429 times.)
« Last Edit: May 04, 2010, 11:13:09 PM by ker2x » Logged

often times... there are other approaches which are kinda crappy until you put them in the context of parallel machines
(en) http://www.blog-gpgpu.com/ , (fr) http://www.keru.org/ ,
Sysadmin & DBA @ http://www.over-blog.com/
ker2x
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« Reply #19 on: May 17, 2010, 02:13:21 PM »

i ran a test and added too much zeros on the parameters.
So i tested 1 billion points at 100.000 maximum iterations (and 5 as "minimum iteration").
(a grand total of 200.000.000.000.000 iterations (worst case, probably much much much less than that))

it took 41.000mn (~28days) of cpu time (on an atom D510 (dual core + HT = 4 "cores")

The resulst is very... useless. i could have the same result with 10mn of computation smiley
But ... well... now i know it !

EDIT : i just checked the picture on a more modern screen (with much more contrast/luminosity) the resulst is not so bad, after all  grin
link to the original 2048x2048 version : http://fractals.s3.amazonaws.com/buddhabrot/buddhabrot-100KBillions.png

EDIT2: on the 2048x2048 version, with a good screen : minibrot everywhere \o/ wonderfull \o/
It wasn't a waste of time  cheesy

compressed 1024x1024 below :
« Last Edit: May 17, 2010, 02:25:24 PM by ker2x » Logged

often times... there are other approaches which are kinda crappy until you put them in the context of parallel machines
(en) http://www.blog-gpgpu.com/ , (fr) http://www.keru.org/ ,
Sysadmin & DBA @ http://www.over-blog.com/
kram1032
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« Reply #20 on: May 18, 2010, 05:56:47 PM »

very nice results smiley
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decayer
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« Reply #21 on: June 10, 2010, 03:26:00 AM »

very good! I just thought the image means flattened. You know why?
And man, it's really fast!
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