OK. Here's my last attempt at trying to explain why this isn't a fractal. This is an image similar to what you posted:

This is what happened after I zoomed in a bit and I used anti-aliasing:

for me i may repeat it seem this is not worse fractal than sierpi?ski carpet

I have no idea why you still think your image is a fractal. The way I see it, what you plotted is a couple of hundred concentric circles, which when sampled with a regular grid result in a spectacular moiré pattern. It's not like we are saying your image isn't pretty: It just has little to do with fractals.

I found this link: http://www.nahee.com/spanky/www/fractint/circle_type.html (Notice the "not a fractal" part.)

I think it is unrelated to sampling on the grid- all in all this is well defined

F(x,y) function for x,y are real, - so sampling to a grid is not important imo, it just blurs the details, dont you think?

Very good info in this link, (i was searching for such references) though here is written ". The resulting image is not a fractal because all detail is lost after zooming in too far. "

Im not sure if this is true, if one will raise the frequenzy of palette

i think the detail depth will probably increase to infinity - so it probably depends how you define this construct

Your function F(x,y) is a continuous function, but when you create your image you sample F(x,y) at discrete points. Each pixel in the image is a sample point of the function. In your first post, for example, you sample F(x,y) at roughly 950 discrete points along both the X and the Y axis. The interference is not in F(x,y) itself, but comes from sampling it at discrete points.

OK. Here's my last attempt at trying to explain why this isn't a fractal. This is an image similar to what you posted:

This is what happened after I zoomed in a bit and I used anti-aliasing:

You got to low frequenzy paltette (*)- I was saing about this, (more than once i think and I see some ignore it ;\ - ) the details will appear if you increase it - if you will ignore this we will not agree here

(same thing with sierpi?ski on mandelbrot if you do only 5 iteration steps

you will get finite complexity)

(*) and maybe to low sampling frequenzy too, if this pattern vanishes

indeed maybe the grid sampling is needed - i dont know if this distortion to circles are so small that this grid sampling shows it

anyway this is strange - do antyaliasing destroyed most of the pattern but leaved some horizontal and vertical line ones? if the rest vanished why the vertical horizontal are still visible?

what way this antyaliasing works here? average of many subsamples per pixel?

on the other way this not changes too much:

if underlying shape is such smooth, indeed the grid sampling should be included in algorith - but this do not change to much only adds some module to formula - sample the result with rectangle grid

you think infinite complexity is not obtainable this way?

Your function F(x,y) is a continuous function, but when you create your image you sample F(x,y) at discrete points. Each pixel in the image is a sample point of the function. In your first post, for example, you sample F(x,y) at roughly 950 discrete points along both the X and the Y axis. The interference is not in F(x,y) itself, but comes from sampling it at discrete points.

Dont think so, Could you explain this, lets say that you are taking

some point x, y = 0.1776527, 0.23876 You say that color value of this point depends on the grid resolution? IMO F(x,y) values are grid independant

Your function F(x,y) is a continuous function, but when you create your image you sample F(x,y) at discrete points. Each pixel in the image is a sample point of the function. In your first post, for example, you sample F(x,y) at roughly 950 discrete points along both the X and the Y axis. The interference is not in F(x,y) itself, but comes from sampling it at discrete points.

Dont think so, Could you explain this, lets say that you are taking
some point x, y = 0.1776527, 0.23876 You say that color value of this point depends on the grid resolution? IMO F(x,y) values are grid independant

what way this antyaliasing works here? average of many subsamples per pixel?

Yes, I took 200 random samples inside each pixel and averaged the colors.

Another proof it's a sampling artifact: Zoom in and out on Álvaro's anti-aliased image with your browser (IE,Firefox, Opera: CTRL + mouse wheel) and watch these circles come and go. One can sometimes even notice a second Moiré effect in a checkerboard fashion probably due to a box filter for the images.