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fractal result by accident


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#1 fir   Members   -  Reputation: -460

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Posted 05 February 2014 - 11:23 AM

I was tinkering a bit with my basic raytracing code and by accident i

received some kind of fractal pattern

 

 ff.jpg

 

does maybe someone know if it has some official name? i think i saw this already in some book or something

 

the code to get this is like i was counting distance from screen points (along the rays) to sphere (this distance should be about 0 to 1000)  then just multiplying this by 255.9

casting to unsigned and adding it like

 
  unsigned color_ = (red<<16) + (green<<8) + (blue);
 
then setting pixel :/ i do not know exactly reason of this outcome but it is funny ;\ (in mathematical way)


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#2 Brother Bob   Moderators   -  Reputation: 8252

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Posted 05 February 2014 - 11:28 AM

Looks like normal sampling aliasing or interference patterns. As the frequency of the rings increase, they approach and pass the limit at which you sample the rings at the pixels.



#3 fir   Members   -  Reputation: -460

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Posted 05 February 2014 - 11:35 AM

Looks like normal sampling aliasing or interference patterns. As the frequency of the rings increase, they approach and pass the limit at which you sample the rings at the pixels.

may be but besides is a some specyfic fractal structure, (type of fractal) probably/maybe has some name



#4 Brother Bob   Moderators   -  Reputation: 8252

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Posted 05 February 2014 - 11:50 AM

Zoom in on those structures and see what happens when you get closer to them. If the patterns change as you zoom in, then this is definitely just normal sampling aliasing. The fact that you only calculate a distance and transforms it into some color means that the pattern should just be circular rings around a center point, but circular patterns with too high frequency for the display produces those particular patterns. Nothing fractal at all about it.



#5 unbird   Crossbones+   -  Reputation: 5115

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Posted 05 February 2014 - 12:12 PM

...probably/maybe has some name.

 
It does: Moiré

#6 fir   Members   -  Reputation: -460

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Posted 05 February 2014 - 12:34 PM

Zoom in on those structures and see what happens when you get closer to them. If the patterns change as you zoom in, then this is definitely just normal sampling aliasing. The fact that you only calculate a distance and transforms it into some color means that the pattern should just be circular rings around a center point, but circular patterns with too high frequency for the display produces those particular patterns. Nothing fractal at all about it.

 

I cannot agree this is not a fractal, iMO this is a well defined fractal.

 

I think this coloring is stable, it is you probably can paint a real wooden

ball this way - this is probably effect of colouring some geometrical surface based on distance to point with cyclic palette - you will get stripes here, if distance would be counted from only one point you will

probbly get centric circles on a ball, but this distance is counted not

from one point but from each screen pixel so it results in such strange fractal (this is what i think i am not sure)

 

zooming the ball I think will not change the effects with covering spray

(just zooming it) but probably with rising the spatial frequenzy of palette wil uncover infinite complexity of the rings... that i suspect



#7 Brother Bob   Moderators   -  Reputation: 8252

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Posted 05 February 2014 - 12:55 PM

Why "I think" and "I suspect" when you can try to verify your claims and be completely confident instead? Zoom in on some part of the image showing a fractal behavior. If it is indeed a fractal pattern, the pattern should remain stable as you zoom in and recalculate the region at a higher resolution.



#8 Brother Bob   Moderators   -  Reputation: 8252

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Posted 05 February 2014 - 01:08 PM

Here's a link for you describing the effect you're getting: clicky. There are some examples near the end showing pretty much exactly your results.

 

You may also be able view the effect, including zooming, on the resolution chart on page 4 in the PDF. The small part in the middle with some circular patterns shows the exact same effect on my screen when zooming out to view the page as a whole. This is because the resolution of my screen is too small to capture the frequencies of the circles. As I zoom in on that part of the figure, the circles become clear and the aliasing effect disappear when the circles are rendered at a higher and higher resolution.

 

Clearly an aliasing effect and nothing fractal about it.



#9 fir   Members   -  Reputation: -460

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Posted 05 February 2014 - 03:06 PM

 

Clearly an aliasing effect and nothing fractal about it.

 

If you say so ;\ (yawn)



#10 Brother Bob   Moderators   -  Reputation: 8252

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Posted 05 February 2014 - 03:21 PM

You asked about an effect that was unknown to you and I gave an answer about an effect that is known to me. You don't have to take my word for it, but I did give you experiments you can perform to either enforce or refute my answer. I have at least provided examples to back my answer up and mentioned experiments you can do to see for yourself. It is not about just believing in my word at that point.



#11 samoth   Crossbones+   -  Reputation: 4792

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Posted 05 February 2014 - 03:22 PM

It does: Moiré

Aye. This.

 

You could see those on TV a lot in the 1970/1980s when TV technology was low-res, low definition interlace stuff, TVs were sucky CRTs, and news anchors would wear checkerboard jackets.

 

Early scanners (when 120 DPI was considered high quality and you had to pull the scanner over the original by hand) had a lot of that too when you used to scan printed media. Nowadays, scanners seem to have some smart kind of supersampling/antialiasing technology built-in.



#12 Ameise   Members   -  Reputation: 737

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Posted 05 February 2014 - 03:24 PM

 

 

Clearly an aliasing effect and nothing fractal about it.

 

If you say so ;\ (yawn)

 

 

Why do you bother asking if you're just going to reject the answers you get if they don't match your predetermined presumptions? I concur that it just looks like a Moiré pattern.


Edited by Ameise, 05 February 2014 - 03:24 PM.


#13 samoth   Crossbones+   -  Reputation: 4792

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Posted 05 February 2014 - 03:30 PM

The effect is so stereotypical retro that it even became a catch-eye effect in a well-known movie trilogy.

 

You know this movie, don't you tongue.png

 

MoireOriginal.JPG



#14 Álvaro   Crossbones+   -  Reputation: 13372

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Posted 05 February 2014 - 04:02 PM


I cannot agree this is not a fractal, iMO this is a well defined fractal.

 

These things have definitions. Start by specifying precisely what set you are talking about, then compute its fractal dimension. If the result is not an integer, you do have a fractal.


Edited by Álvaro, 05 February 2014 - 04:02 PM.


#15 fir   Members   -  Reputation: -460

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Posted 06 February 2014 - 01:00 AM

 



I cannot agree this is not a fractal, iMO this is a well defined fractal.

 

These things have definitions. Start by specifying precisely what set you are talking about, then compute its fractal dimension. If the result is not an integer, you do have a fractal.

 

 

i dont know how to count a dimension do you know how to count this based on that picture?


Edited by fir, 06 February 2014 - 01:03 AM.


#16 fir   Members   -  Reputation: -460

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Posted 06 February 2014 - 01:05 AM

 

...probably/maybe has some name.

 
It does: Moiré

 

this is not this thing, as i said the thing is a result of normal colorizing the surface with a stable preducted palette, no 'border' artifacts or interferency things



#17 LorenzoGatti   Crossbones+   -  Reputation: 2709

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Posted 06 February 2014 - 02:46 AM

 

 

...probably/maybe has some name.

 
It does: Moiré

 

this is not this thing, as i said the thing is a result of normal colorizing the surface with a stable preducted palette, no 'border' artifacts or interferency things

 

As befits an encyclopedia, the linked Wikipedia article takes a narrow and precise view of what a Moiré pattern is, However, it's common to refer to most interference patterns as Moiré patterns, because they are essentially similar patterns regardless of the type of interference.

And aliasing is an interference pattern, between the sampling points and the features of the continuous signal.

In this case you are sampling (at pixel location) a wildly wobbling and discontinuous signal: the quantization error obtained by converting the eye-sphere distances to integers.


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#18 fir   Members   -  Reputation: -460

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Posted 06 February 2014 - 03:32 AM

 

 

 

...probably/maybe has some name.

 
It does: Moiré

 

this is not this thing, as i said the thing is a result of normal colorizing the surface with a stable preducted palette, no 'border' artifacts or interferency things

 

As befits an encyclopedia, the linked Wikipedia article takes a narrow and precise view of what a Moiré pattern is, However, it's common to refer to most interference patterns as Moiré patterns, because they are essentially similar patterns regardless of the type of interference.

And aliasing is an interference pattern, between the sampling points and the features of the continuous signal.

In this case you are sampling (at pixel location) a wildly wobbling and discontinuous signal: the quantization error obtained by converting the eye-sphere distances to integers.

 

 

This is not interference involved also not precision errors or something, this is just a stable way of colorisation of the sphere also i think it has an infinite indepth complexity here (if you wil rize up the palette frequenzy to infinite, as i said, ), here is some 'zoomed' example yet

 

some.jpg



#19 Brother Bob   Moderators   -  Reputation: 8252

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Posted 06 February 2014 - 03:53 AM

This is not interference involved also not precision errors or something, this is just a stable way of colorisation of the sphere also i think it has an infinite indepth complexity here (if you wil rize up the palette frequenzy to infinite, as i said, ), here is some 'zoomed' example yet

 The circles form one pattern, and the pixels forming the discrete sampling grid is the second pattern. The interference is implicit from the intersection between the two patterns when you sample the continuous circle pattern at the discrete pixel grid.
 

attachicon.gifsome.jpg

Overlay that image and the one from your first post and you'll see that the interference patterns, or fractals if you want, are not the same; neither at the equivalent scaled location or at the equivalent scaled size. Your patterns are thus resolution dependent. That's precisely how interference works.



#20 fir   Members   -  Reputation: -460

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Posted 06 February 2014 - 04:06 AM

 

This is not interference involved also not precision errors or something, this is just a stable way of colorisation of the sphere also i think it has an infinite indepth complexity here (if you wil rize up the palette frequenzy to infinite, as i said, ), here is some 'zoomed' example yet

 The circles form one pattern, and the pixels forming the discrete sampling grid is the second pattern. The interference is implicit from the intersection between the two patterns when you sample the continuous circle pattern at the discrete pixel grid.
 

attachicon.gifsome.jpg

Overlay that image and the one from your first post and you'll see that the interference patterns, or fractals if you want, are not the same; neither at the equivalent scaled location or at the equivalent scaled size. Your patterns are thus resolution dependent. That's precisely how interference works.

 

 

I changed the palette frequenzy up 5times (by putting the ball more far now its centre is 5 km far and has a radius of 3.5 km)  in the second picture as i said more details is wisible when rising up the palette frequenzy - what is interfering with what? (I do not see a need of talking 

about this interferentions here, i do not see them, it would be better to talk about math structure of this pattern, but i m not to much educated in hyperbolic geometry or such things)

 

ps probably i could rise up the visual effect by defining nicer palette 

(but not sure if got a time to do this today)


Edited by fir, 06 February 2014 - 04:09 AM.





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