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Author Topic: BuddhaBrot!  (Read 7289 times)
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emmmile
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« on: June 21, 2010, 11:14:38 PM »

Hi everybody,

this is my first post.  cheesy


Some months ago I wrote a BuddhaBrot C++ renderer with possibility of zooming and scrolling.
I loved the pictures that can be displayed so I wanted to share something here!!
This is the minibrot centered at (-1.7674, 0) magnified about 20000 times (magnification is a number of my program, first question: there is an absolute way to define magnification?):



Look at the heart at the centre of the image  Azn..
I set different iterations lenghts for Red, Green and Blue, respectively (about) 1000000, 60000, 1000.
I hope you like it..

Emilio
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Sockratease
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« Reply #1 on: June 21, 2010, 11:39:47 PM »

Hello and Welcome to the forum!

Nice image   afro

I can't help with your question, but there are many here who surely can!

In fact, I suspect Fractal Woman will be interested.  She's the person who coined the term "BhuddaBrot" - so let's hope she takes notice.
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emmmile
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« Reply #2 on: June 22, 2010, 01:12:38 AM »

Thank you!  smiley

So I'll wait for their reply! wink In the meanwhile I'm trying to make a portable executable of my program or find an easy way to compile it from the source code so I can share it!
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Rathinagiri
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« Reply #3 on: June 22, 2010, 03:50:46 AM »

Nice image.
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reesej2
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« Reply #4 on: June 22, 2010, 09:35:15 AM »

There is a standard for magnification, but I've never understood it... something to do with angles and similar... Brilliant picture though!
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cKleinhuis
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formerly known as 'Trifox'


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« Reply #5 on: June 22, 2010, 10:08:40 AM »

hello and welcome to the forums,

what seems to be the problem with magnification ?

in my eyes there are 2 common ways to define a rectangle of magnification, the first would be to use a rectangular region, defined by the upper left and lower right corner, these ranges have to be mapped to your rendering resolution ( delta/resolution = step length ) , if using rotations with this method, the interpolation is not just on a single axis real/imaginary it is a line equation used to go through the region ...

another way and a little easier to use way of defining the magnificaiton is by using a center point, then you would have (0,0) as center, and e.g. 1 as scale factor for the normal view, again you have to define a function wich maps pixel coordinates to real/imaginary coordinates, basically, this would look something like:

mapPixelToComplex(x,y){
// normalize input to a region of (0,0)-(1,1)
real =  (x/pixelWidth)*magnification + centerx
imag =  (y/pixelHeight)*magnification + centery

}

this should work, eventually you want to map your input range to (-1,-1) (1,1) meaning that the upper left of your image is (-1,-1) normalized coordinate, and lower right is (1,1) using this way you got the (0,0) center point exact in the middle ouf your image ... including transformations in this method is far easier than the other ...

it could be discussed which method is faster ... but i just wanted to show you some methods ....
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aluminumstudios
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« Reply #6 on: June 22, 2010, 11:57:04 AM »

How long did it take to render?
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emmmile
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« Reply #7 on: June 22, 2010, 01:33:07 PM »

Thank you Trifox for the explainations, and thank you for the replies  Azn.

I think I'm using the second concept of magnification you presented. If I have a magnification of 1 I will see 1 unit (on the graph) on exactly 1 pixel. Infact my base zoom for view the buddhabrot is about 200.

How long did it take to render?

About 10-15 minutes.
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johandebock
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« Reply #8 on: June 22, 2010, 01:42:38 PM »

Is it calculated with uniform sampling within real:[-2.0, 2.0] imag:[-2.0, 2.0], or with some statistical optimizing to get more paths crossing the region of interest?

Renderings do look different when using different rendering techniques I've noticed with my BuddhaBrot renderer.
A zoom unit is defined the following way in my program:
When viewing [-2.0, 2.0][-2.0, 2.0] the zoon factor is x1.
When viewing [-1.0, 1.0][-1.0, 1.0] the zoon factor is x2.
When viewing [-0.5, 0.5][-0.5, 0.5] the zoon factor is x4.
And so on...
« Last Edit: June 22, 2010, 01:49:04 PM by johandebock » Logged

emmmile
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« Reply #9 on: June 22, 2010, 02:05:43 PM »

I used the metropolis method that I found here: http://www.steckles.com/buddha/ and a similar approach to find points with an orbit that crosses the window, however these points are chooesen randomly!

Maybe we are using also different tecniques for processing the colors, lightness and contrast of the image..
« Last Edit: June 22, 2010, 02:08:46 PM by emmmile » Logged
johandebock
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« Reply #10 on: June 22, 2010, 02:21:24 PM »

Yes coloring is also important, have you also have the regular algorithm in your renderer (would take a lot more time to calculate)?
It would be interesting to see if there is any difference in the final renderer with all other parameters the same.
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emmmile
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« Reply #11 on: June 22, 2010, 02:47:37 PM »

Yes in this case of zoom it would take a lot more time, and the result is also a little bit different.. If I have time I'll post an example.
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cKleinhuis
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« Reply #12 on: June 22, 2010, 03:16:21 PM »

you know, the buddhabrot method works for any fractal type, even alternating ones, has anyone implemented different formulas to examine ?!
i once wrote a buddhabrot renderer with alternating fractals, i hope you do so also wink
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divide and conquer - iterate and rule - chaos is No random!
emmmile
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« Reply #13 on: June 22, 2010, 03:40:56 PM »

you know, the buddhabrot method works for any fractal type, even alternating ones, has anyone implemented different formulas to examine ?!
i once wrote a buddhabrot renderer with alternating fractals, i hope you do so also wink

I tried also the anti-buddhabrot and other completely different formulas (not fractal also XD) and they work well. Sincerally I didnt spent a lot of time on these variants tongue stuck out. However these are some results (I don't remember the formulas  cry ):





And this is the region near (0.0787338, 1.02135) rendered in the anti-buddhabrot mode:

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emmmile
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« Reply #14 on: June 22, 2010, 03:53:18 PM »

Yes in this case of zoom it would take a lot more time, and the result is also a little bit different.. If I have time I'll post an example.

Ok this is the difference between the normal algorithm and metropolis (i rendered the whole fractal and I left all other options to the same value). Normal:



Metropolis:



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