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I seen this fractal in a dream although I never mess with fractals and only familiar with the concept I seen a symbol with many thousands of symbols within it branching to form an endless web of a repeating pattern.

I drew below the symbol and how it repeats. Would anyone help me to make this fractal so that I can see it in its true glory?

I would appreciate it more than I could say.

(http://img132.imageshack.us/img132/9638/sigiln.jpg)

Hello and Welcome to the forum!

Your image appears to be more of a "formula object" than a Fractal.  Not sure of how to reproduce it any better than you have already done.  What are you looking for?  

Just use the pattern as a tile, and create a larger resolution image?  I have an image editor that can tile images in 3 different ways (aligned, brick, and mirrored) and could give that a try to make a large image if that is what you are looking for.

But I have no idea how to describe the actual pattern mathematically...

Maybe one of our Long-Haired Math Wizards will know?

I fail to understand where is the iterative process in your drawing. Do you mean the smaller and smaller circles?

well the main pattern is the half circle not a full circle. The half circle stretches endlessly behind it is an echo of itself endless as well. The main pattern is the 4 half circles meeting. Then the echo off of them. I hope I am making sense. Feel free to ask more questions.

hmmm...
to me, it looks a lot like a wavelet-based pattern... :)

something like this:


If you then colour it according to the ripples, you probably get a pattern, not too different from this.

Greetings, and Welcome to this particular Forum !!!    :)

All that I see here is a portion of a geometric pattern that has been overlaid upon itself.  And in this instance, that geometric pattern happens to appear as concentric circles (http://en.wikipedia.org/wiki/Concentric).  Most any basic geometric shape could be used for such a pattern.

I have created similar images using XenoDream (http://www.xenodream.com/):

(http://www.nahee.com/Fractals/XenoDream/Images/Celtic_Knot.jpg)

(http://www.nahee.com/Fractals/XenoDream/Images/What_A_Mesh.jpg)
 

Now here is something in the same vein, but using a squarish shape, with blue colored concentric circles (in the similar pattern that you gave us) "painted" over the top of the pattern:

(http://www.nahee.com/Fractals/XenoDream/Images/Arabesque-03-c.jpg)

You can find others like this at the following web page:
    http://www.nahee.com/Fractals/XenoDream/Arab_Baroq.html (http://www.nahee.com/Fractals/XenoDream/Arab_Baroq.html)
 

I have cut up the image to show the main pattern. (http://i47.tinypic.com/2j42f5l.jpg)

After taking your original image and tiling it across a block, I can clearly see that this was not concentric circles but in reality a spiral, with the line thickness diminishing slightly with each complete revolution:

   (http://www.nahee.com/Stuff/sigiln-tiled.gif)
 

Its not a full circle or tiles. You have the main pattern of which i have in the 4 half circles. These edges stretch to whatever edge and echo backwards to form the web of which i did a partial echo on the original picture. On a full echo it would be a complete web that looks like a dimension being stretched from the middle point. In a fractal this should look more so as a endless web. Much like how you did this image but not the overlapping of the center point.

(http://www.nahee.com/Fractals/XenoDream/Images/What_A_Mesh.jpg)

I was thinking of perhaps finding the "formula?" for it and putting it to work on how these fractals are generated..
(http://www.fractalforums.com/gallery/1/900_13_01_10_2_59_30.png)

What you're talking about then rather is like this...



if x=]-1,1[ or y=]-1,1[
then reflect back into that and add.
wolfram alpha shifted sinc (http://www.wolframalpha.com/input/?i=3Dplot+sinc%28pi*%28sqrt%28%28x%2B1%29%C2%B2%2By%C2%B2%29-1%29%29%2Cx%3D-2...2%2Cy%3D-2...2) <- here is the graph of just one of the functions. It's impossible to do all four functions over there: It tells me, it "doesn't know, what I mean", then.

However, it is possible to do a double wave...
two shifted sincs overlay (http://www.wolframalpha.com/input/?i=3Dplot+sinc%28pi*%28sqrt%28%28x%2B1%29%C2%B2%2By%C2%B2%29%2B1%29%29%2Bsinc%28pi*%28sqrt%28%28x-1%29%C2%B2%2By%C2%B2%29%2B1%29%29%2Cx%3D-2...2%2Cy%3D-2...2)

different overlay (http://www.wolframalpha.com/input/?i=3Dplot+sinc%28pi*%28sqrt%28%28x%2B1%29%C2%B2%2By%C2%B2%29%2B1%29%29%2Bsinc%28pi*%28sqrt%28x%C2%B2%2B%28y%2B1%29%C2%B2%29%2B1%29%29%2Cx%3D-2...2%2Cy%3D-2...2)

When ever the ripple is on a high point, you colour it white and on a lowpoint, you colour it black.
Keep in mind, that this is not with the reflections.

The flower of life. It is sacred geometry. it is very usual. look into it. Some people call them mandalas.

it's not quite the flower of life by how it's described. Close but not quite.

http://www.world-mysteries.com/sar_sage1.htm

I used to see it when I was young. It was like rings of red clouds. I called it the "doughnuts".

Perhaps something like Fractint's "Plasma Cloud", in polar coordinates, with a dimension 1.5 (for randomness) in the angular direction and a dimension close to 1 (for nearly smooth waves) in the radial direction.

I see you must be new to the world of fractals, because that is not a fractal. Just a nice looking fairly complex shape.
When I have no idea what to draw, sometimes I just draw some random type of fractal. That is, something with self similarity unlike that image.