Newbie: How to map colors in the Mandelbrot set?

[Nahee_Enterprises]

But Duncan's seems to show more of the details than yours does.  It is almost as though yours has been anti-aliased to the point of blurring.

as an antialiasing fetishist, i must say iev's render is exceptionally well done.

edit: take a close look at the edges, you'll find they are much better defined; moreover, the interior gradients are much smoother and the whole thing has more contrast and is very crisp.  where do you see loss of detail?

Yes, I am aware of your viewpoint on anti-aliasing.  It is the same as the one Erik Nathan Reckase has towards images.  But everyone is entitled to their opinions on how an image should be handled.   

And I have already said that the coloring of IEV's image was much better and quite like the original reference.  I made no complaints about the gradients, smoothness, contrast, etc...

IEV's edges are better defined when it comes to the areas where the inside and outside of the M-Set meet.  This is where it shows as being "very crisp".

It is the actual spirals, filaments, and other such details which are blurred to the point of appearing as if viewed by a near-sighted individual that is not wearing their corrective lenses.  Which means their can be no "very crisp" portions visible.  (BTW, my definition of "crisp", when it comes to images, is that there are conspicuously clean areas which are marked by clarity, pleasingly firm.  Another words, pretty much as the dictionary defines the word "crisp".)

My personal preference is less softness and less blurring.  I like sharpness and edges.   

I find those that prefer blurred images usually enjoy "flame" fractals more so than other fractal image types.

[lycium]

Yes, I am aware of your viewpoint on anti-aliasing.  It is the same as the one Erik Nathan Reckase has towards images.

um, what is my viewpoint on antialiasing? and erik reckase's on images?

My personal preference is less softness and less blurring.  I like sharpness and edges.   

good antialiasing has everything to do with sharpness and edges, really: http://graphics.stanford.edu/~mmp/chapters/pbrt_chapter7.pdf

in fact it's probably because almost no one on earth takes proper care wrt antialiasing that you associate it with blurring. it really is both a science and an art, not to be mocked...

I find those that prefer blurred images usually enjoy "flame" fractals more so than other fractal image types.

there are few things i dislike more than blurred images. antialiasing is first and foremost a matter of accuracy and precision, and blurring is totally out of the question.

the fundamental distinction is this: you can bandlimit a signal, performing proper reconstruction up to the nyquist limit, without blurring the image needlessly.

[Duncan C]

Yes, I am aware of your viewpoint on anti-aliasing.  It is the same as the one Erik Nathan Reckase has towards images.

um, what is my viewpoint on antialiasing? and erik reckase's on images?

My personal preference is less softness and less blurring.  I like sharpness and edges.   

good antialiasing has everything to do with sharpness and edges, really: http://graphics.stanford.edu/~mmp/chapters/pbrt_chapter7.pdf

in fact it's probably because almost no one on earth takes proper care wrt antialiasing that you associate it with blurring. it really is both a science and an art, not to be mocked...

I find those that prefer blurred images usually enjoy "flame" fractals more so than other fractal image types.

there are few things i dislike more than blurred images. antialiasing is first and foremost a matter of accuracy and precision, and blurring is totally out of the question.

the fundamental distinction is this: you can bandlimit a signal, performing proper reconstruction up to the nyquist limit, without blurring the image needlessly.

lycium,

Your points about good antialiasing are well taken. Good antialiasing should make edges look smoother (less "jaggy") without making them look blurry.

To my eye, though, the filaments in iev's  post look soft, like they were processed with a low radius gaussian blur. I'm not sure why they look that way, since the boundary of the M set is quite crisp.

iev, do you have any idea why the edges of the filaments in your image seem slightly blurry? All the color schemes I tried with that image left the edges clearly defined.



Duncan

[lycium]

Your points about good antialiasing are well taken. Good antialiasing should make edges look smoother (less "jaggy") without making them look blurry.

that's exactly it; aliasing is just a fancy word (in the context of spectral/fourier analysis) for jaggies

To my eye, though, the filaments in iev's  post look soft, like they were processed with a low radius gaussian blur. I'm not sure why they look that way, since the boundary of the M set is quite crisp.

the "gaussian hump" (kinda lewd name for a filter kernel if you ask me) is actually one of the better filters to use for fractals, because:

1. filters having negative lobes are unsuited to fractal boundaries <insert long fourier analysis here>
2. the gaussian filter is radially symmetric (cf. separable like most other filters) and much smoother than the box or tent filters, making it well suited to combat the (infinitely) high frequency variation at fractal boundaries.

i can almost hear people in the audience unfamiliar with signal processing thinking "but gaussian filters blur". this is where one has to fight the fame of photoshop: yes, it is a blurring filter in photoshop, but that's not how it's supposed to be used here! as a photoshop filter, you take a very wide gaussian (say 10+ pixels in diameter) and convolve all the surrounding pixels with it. as an antialiasing filter, you take a very narrow gaussian (say sqrt(2) pixels in diameter) and convolve the underlying continuous function with it, so as to produce a bandlimited sample which will not alias.

i really cannot overstate the difference between the two approaches; one is a process which destroys information, and the other is one which greatly increases the information content. aliasing is not only ugly, it's information massacre!

<rant>
life becomes more complicated once you've studied information theory and signal processing. i nearly got thrown out of the cinema while watching "enemy of the state" (quite a few years back as a hormonal teenager, mind ) - in the scene where they take a photo, zoom in 1000x and spin it around in 3d, i just started yelling "booooollocks!" etc. i know it wasn't appropriate, but sometimes i just can't help myself; fortunately i got it under control
</rant>

[iev]

Although I had it in my mind, I finally forgot to mention this in my last message. The original image I got from my program was 2048x1536 pixels. I used GIMP to resize it to 800x600, in order to post it here. If I create directly a 800x600 image, it is not as detailed and the colors don't change as smoothly. This happens of course because each pixel now corresponds to a larger "square" of the area in the complex plane under consideration. Although I don't have the original image handy, I remember that resizing the image resulted in this slight blurring.

I hope this clarifies things.

[lycium]

I hope this clarifies things.

resampling the image didn't cause any blurring, it caused antialiasing... oh well, i give up.

[iev]

lycium,

Please don't get angry at me. I never claimed to be an image processing expert or even to know concepts about it. The proof is that I don't know what the difference between blurring and antialiasing is. It might seem very basic to you, but it is not to me.

I assume that you will have the same reaction if I start mentioning concepts about parallel processing, which is my area  Please realize that creating these images is not a requirement for me. I am more interested in parallelizing the algorithm and this is where I need the good results. If I get some nice images and can put them in some publication, it will be just a bonus. It will not help me (in my work) if what we saw in my image is antialiasing or blurring.

In any case, I appreciate your effort to educate us on these concepts!

[lycium]

i'm not angry at all, just rolling-eyes-disappointed perhaps   just supersampling instead of increasing the resolution will do much to reduce your benchmark's i/o requirements, for example.

i know a decent bit about parallel programming, having writing a distributed ray tracer in high school to run on a cluster of amd machines in my computer lab at the time, and then all the way up to an mpi-based cluster at a physics department's supercomputing lab. i suspect you may have conducted your research on such a system; i'm actually a ray tracing guy, not a fractal guy, and parallel computing comes naturally to ray tracers (it's a so-called "embarassingly parallel" algorithm, in your terminology).

please don't get the impression that all people posting on forums about fractals know only about fractals many of us post on several forums, and even do stuff for a living

[Duncan C]

iev,

I found this old thread and decided to try another crack at your sample Image. I think i got really close.

Here is the image from Wiki:



And here's what I came up with:


The image gets a little washed out when I post it to the internet, unfortunately. I'm not sure why. I made sure the image was in sRGB.

I used 3 gradients in my image: Yellow to orange for pixels very close to the set, orange to very dark orange, then very dark orange to black.



Duncan C