Future application of fractal maths in computer...imaging (I think) *spawn

steampoweredgod said:
fractal is perfect exact mathematical solution.
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Of those models that can be epxressed as fractals. Some (lots) of datatypes can't. The perfect exact mathematical solution for a cube or sphere isn't a fractal.

And if you have a massive array if Retina displays, 2,000,000 by 1,500,000 pixels say, and a source image of 1024x768, upscaling it to that display will result in low-resolution mess up close. And if you take a 2,000,000 x 1,500,000 source image and compress it, you are employing lossy methods. I dare say a fractal compression and upscale would give better results than a wavelet compression and fancy upscale, but it's still a limited solution.
 
Shifty Geezer said:
Of those models that can be epxressed as fractals. Some (lots) of datatypes can't. The perfect exact mathematical solution for a cube or sphere isn't a fractal.

And if you have a massive array if Retina displays, 2,000,000 by 1,500,000 pixels say, and a source image of 1024x768, upscaling it to that display will result in low-resolution mess up close. And if you take a 2,000,000 x 1,500,000 source image and compress it, you are employing lossy methods. I dare say a fractal compression and upscale would give better results than a wavelet compression and fancy upscale, but it's still a limited solution.
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Watch documentary, mathematical monsters or fractals do away with incommesurability and allow 1 to 1 representation of diameter to circumference, and diagonal to side triangle representation. yOur traditional mathematical abstraction introduces the mess of incommesurability, which in all fairness is not perceived or produced even in digital systems.

Ponder if a human artist given infinite time and resources was doing faithful upscaling with likely fractal-like(brain structure exhibits vast self reference | recurrent connectivity) computation or thought, would he introduce distortion?
 
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steampoweredgod said:
Try and handle a a retina(ipad) wall if you can.

In information transmission, reception and emission, fractal is perfect exact mathematical solution.

All in the computer is information, it is very possible that fractal encoding is also perfect method, though this has yet to be seen.

Remember that the brain is nothing more than a network, which seems to use fractal structure in its design.

Infinite resolution will always surpass any finite resolution however big.
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We already have the 'infinite resolution' version of the scene, why would we want a new method to invent incorrect data to replace what we already have?
 
Shifty Geezer said:
You're having a giraffe, right? "Perfect resolution independence"?? You cannot describe missing detail with a fractal formula, unless you're original material was created in a way that matches a fractal description. Enlarging with a fractal upscaling algorithm removes the obvious blocks and produces something that has detail, but it's not the same detail that the source had. You cannot take a photograph of a beach scene and use fractals to zoom in on a person and recreate their face, and then zoom in on the reflection in their sunglasses of the paper they were reading to read the text!

Fractal upscaling is always going to be massively more complex than a simple blinear or bicubic upscale. It makes more sense to invest processing time elsewhere (shading, blending multiple textures for variety) than making a few textures look less blurry up close.
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Say it isn't so, I saw an episode of CSI where they did this and you could read the text on that newspaper! :)

I think the steampoweredgod is getting confused between two different things.
These bitmap images that use "fractals" are not the same thing as a maths formular for fractals.
The images are finite, while the maths formular is infinate - they are totally different.

I have not seen the documentry but it probably lumps them together as one.

Now it is feasable you could describe an image with a complex formulae but it would be so massivly complex it would not give you any advantage.
 
mikiex said:
Say it isn't so, I saw an episode of CSI where they did this and you could read the text on that newspaper! :)

I think the steampoweredgod is getting confused between two different things.
These bitmap images that use "fractals" are not the same thing as a maths formular for fractals.
The images are finite, while the maths formular is infinate - they are totally different.

I have not seen the documentry but it probably lumps them together as one.

Now it is feasable you could describe an image with a complex formulae but it would be so massivly complex it would not give you any advantage.
Click to expand...

The arbitrary image is turned into precise specific corresponding fractal formula which grants resolution independent representation. Video fractal compression is also possible for arbitrary videos.

It won't add anything that ain't their implicitly(detail that any artist could predict is originally there). The formula is not also infinite it merely has self-reference and is quite finite and simple easily computable.

And would allow the image to remain perfectly legible and understandable, with proper proportions, even if use a giant layer of atoms the size of the distance between earth and the sun to generate a high resolution image bigger than this planet.

That is the nature of fractal representations that you can use more atoms then in the visible universe to generate a screen of x pixels, and the image will be perfectly scaled and legible, as happens with vector graphics representations of text.



dealing with incommesurability, pi the square root of two, and allowing 1 to 1 mapping between diameter or side and circumference or diagonal is beautiful and shows that a digital procedure may generate perfect triangle or circle.
There are 2 documentaries one more ancient the other more novel. Fractal architecture abounds in the solutions of evolution throughout the ecosystem, and even your own human body and brain
 
steampoweredgod said:
The arbitrary image is turned into precise specific corresponding fractal formula which grants resolution independent representation. Video fractal compression is also possible for arbitrary videos.

It won't add anything that ain't their implicitly(detail that any artist could predict is originally there). The formula is not also infinite it merely has self-reference and is quite finite and simple easily computable.

And would allow the image to remain perfectly legible and understandable, with proper proportions, even if use a giant layer of atoms the size of the distance between earth and the sun to generate a high resolution image bigger than this planet.

That is the nature of fractal representations that you can use more atoms then in the visible universe to generate a screen of x pixels, and the image will be perfectly scaled and legible, as happens with vector graphics representations of text.



dealing with incommesurability, pi the square root of two, and allowing 1 to 1 mapping between diameter or side and circumference or diagonal is beautiful and shows that a digital procedure may generate perfect triangle or circle.
There are 2 documentaries one more ancient the other more novel. Fractal architecture abounds in the solutions of evolution throughout the ecosystem, and even your own human body and brain
Click to expand...

Vector text has infinite resolution and it has nothing to do with fractals, its just math
 
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mikiex said:
Vector text has infinite resolution and it has nothing to do with fractals, its just math
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Related to this, in a previous life, I helped develop a vector graphics rendering/painting system where the geometry and rendering was done in float (with coverage-based AA). The demos would usually contain models at multiple scales and so things would keep on appearing as you zoomed further and further in....until you got to the point where the floats hit the denorm limit and suddenly all the smooth spline edges became saw teeth! :)
 
Simon F said:
Related to this, in a previous life, I helped develop a vector graphics rendering/painting system where the geometry and rendering was done in float (with coverage-based AA). The demos would usually contain models at multiple scales and so things would keep on appearing as you zoomed further and further in....until you got to the point where the floats hit the denorm limit and suddenly all the smooth spline edges became saw teeth! :)
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You found the Atoms then ! :)

I remember in school we had this CAD drawing program on the BBC that had a weird joystick, I was facinated by hiding little bits of text at microscoptic level. Id be quite interested in a game where you zoom in on things.
 
steampoweredgod said:
The arbitrary image is turned into precise specific corresponding fractal formula which grants resolution independent representation. Video fractal compression is also possible for arbitrary videos.
Click to expand...
Exactly the same way as you can have hash collisions you WILL have "fractal collisions" when trying to represent something with less data than in the original.

Also,
http://www.femtosoft.biz/fractals/fractal.html
"I've been able to achieve compression on the order of a gif or jpg file."

I tried his delphi app to compress a 1680x1050 minecraft screenshot and it tells me it takes around 1000 minutes on a 2.8GHz i7 :LOL:

Doesn't sound all that efficient to me. Do you happen to have any better stuff I can play around with or does it all exist just in theory?

[edit]
This just keeps on getting better and better.

I tried compressing a 400x220 picture (same screenshot resized) and it gave me 61.1kb file. Original .bmp was 257kb, png 102kb and jpg at 95% quality 39kb so I thought it wasn't quite a disaster at reducing the file size.

And then I decompressed the fractal to find out that it's only grayscale! Same image in grayscale BMP: 86.9kb, png: 48.1kb and jpg 33.9kb. So yeah, a lossless PNG is better than fractal, at least for this image:
2012-02-25_12.29.23.png


It would be fun to test it with actual photos or at least some 2kx2k textures used in games. I wouldn't be surprised if the result is even worse due to minecraft having so huge texel sizes on screen.
 
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hoho said:
Exactly the same way as you can have hash collisions you WILL have "fractal collisions" when trying to represent something with less data than in the original.

Also,
http://www.femtosoft.biz/fractals/fractal.html
"I've been able to achieve compression on the order of a gif or jpg file."

I tried his delphi app to compress a 1680x1050 minecraft screenshot and it tells me it takes around 1000 minutes on a 2.8GHz i7 :LOL:

Doesn't sound all that efficient to me. Do you happen to have any better stuff I can play around with or does it all exist just in theory?

[edit]
This just keeps on getting better and better.

I tried compressing a 400x220 picture (same screenshot resized) and it gave me 61.1kb file. Original .bmp was 257kb, png 102kb and jpg at 95% quality 39kb so I thought it wasn't quite a disaster at reducing the file size.

And then I decompressed the fractal to find out that it's only grayscale! Same image in grayscale BMP: 86.9kb, png: 48.1kb and jpg 33.9kb. So yeah, a lossless PNG is better than fractal, at least for this image:
2012-02-25_12.29.23.png


It would be fun to test it with actual photos or at least some 2kx2k textures used in games. I wouldn't be surprised if the result is even worse due to minecraft having so huge texel sizes on screen.
Click to expand...

Take a look at this page
http://users.senet.com.au/~mjbone/Fractals.html

They have links to the early iterated systems exe;s who originally came up with the method and format FIF,
It was combined as a compression / resize originally. But these days the same tech continued "Genuine Fractals" and the emphasis is on the resizing it became "Perfect Resize": http://www.ononesoftware.com

How good is it? Thats a debate, I can't say I've seen a decent real test - normally they just compare it with the some what dated photoshop resampling
 
hoho said:
Doesn't sound all that efficient to me. Do you happen to have any better stuff I can play around with or does it all exist just in theory?
Click to expand...
I'm afraid steampoweredgod is not available to answer at the moment. If you'd like to leave your name and number, he'll never get back to you...

mikiex said:
How good is it? Thats a debate, I can't say I've seen a decent real test - normally they just compare it with the some what dated photoshop resampling
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Even then, the fractal enlargements are clearly upscaled. They aren't filling in any convincing details. I'm wondering if a simple bicubic upscale with a little blur and peturbation wouldn't give the same sorts of results at a lot less effort.

Fundamentally, I'm not seeing any application of fractals in image resizing or storage. They'll remain used for procedural content creation and that's about it.
 
Steamy's problem is his argument is based on what he imagines fractal compression to be, not what it actually is.
 
Gerry said:
I'm not sure that was his only problem to be honest.
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What do you mean? Are you saying this isn't normal!?

http://steampoweredgod.blogspot.com/2012/03/so-it-seems-people-have-accelerated.html

So it seems people have accelerated their rate of completion of celestial sword project
Then it is time for me to force life through my decaying veins, and start my ritual of ascension, coding, godlike, beyond godlike speed coding, faster than a god of code, faster than the god of the wired, faster than a superintelligence, due to perfect player code base library access hyperturing capability through hilbert's dream, wonderland through the looking glass alice lies.
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Dunno seems pretty legit stuff to me...

:)
 
fractal's place is in procedural textures/geometry
microtextures aren't so far off
see allegorithmic middleware
fractals are ok for filling in the gaps but don't represent true information

regarding the OP you'd just smooth and/or apply jitter to geometry (displacement maps) for resolution independence
 
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I'm just pulling stuff out my ass here... but...

So you can project spatial data to a frequency domain with Fourier transforms. Can you similarly project spatial data to some, oh let's call it 'recursive domain' where the basis are recursive patterns? Does it even make any sense?
 
jameszhao said:
I'm just pulling stuff out my ass here... but...

So you can project spatial data to a frequency domain with Fourier transforms. Can you similarly project spatial data to some, oh let's call it 'recursive domain' where the basis are recursive patterns? Does it even make any sense?
Click to expand...

micro textures on displacement maps for objects that are supposed to be rough
guess the type of micro texture per texel from the surrounding area of the real modeled detail or allow artists to paint it
 
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