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This fractal was rendered in FractalWorks, a free, high performance fractal renderer for Macintoshes.

It is a Julia set fractal, rendered in 3D using distance estimate values for heights.

The seed point for the Julia set is from a tendril on an "elephant" on the largest baby Mandelbrot on the real axis. (@ -1.74948424768, 0.00014462615026 i, real width 1e-10)

(http://www.pbase.com/duncanc/image/99902119/original.jpg)


I really like the textures on this image.

This is really gorgeous -- very nicely composed both in color/lighting and subject.

My only suggestion would be to make the fractal rendering extend all the way to the edge of the image if possible so there's no cut-off effect, or crop it so the edges aren't visible...minor thing.

What software did you use to do this?

And again a great work with your program - my compliments :-)))
Margit

HPDZ,

The image was generated with FractalWorks, a free, high performance fractal renderer I've written for Macintosh computers. I should have said that in the description. I've added that info now.


Duncan C

the image is again brilliant, great work!

@hpdz

the problem with the outside areas is, that it can be a pretty big range to calculate the whole visible area,
some attemps use level of detail, but i do not know of a program which could extend to the horizon

@duncan
an option would be cool that the 3d rendering continues to fill out visible squares, after it has finished the main square

My app starts with a 2D plot, and then does a 3D rendering of it. Once you've created a 3D plot you can pan the camera around the view, zoom in our out, and define a crop rectangle that determines the region of the plot that gets saved to a JPEG or TIFF file.

It was pretty easy to create a variant that extended all the way to the edge of the screen. Is this what you had in mind?
(http://www.pbase.com/duncanc/image/100619984/original.jpg)

It's a question of taste which version you like better. Personally, I rather like the first one. I've thought about adding an option to turn the height map (which is basically a stretched piece of fabric) into a solid with a base, so it would look like the top was carved into a block of material. I don't always want that, though, because images like the 3D flowers (http://www.pbase.com/duncanc/image/97630147) look better when they are a 2D sheet stretched in 3 dimensions.


Regards,

Duncan C

Great! Thanks for taking the time to do this. It is exactly what I had in mind. You're right, of course, it's more a matter of taste, but the border is artificial, so my feeling is that it's better to have the fractal image run all the way to the edge of the rendering...

I really must explore this 3D-ization business. Many of the ones I've seen have been kind of dorky, so I've avoided the whole format, but you've rekindled my interest. It's also a lot of really cool math to run through....

Here's the example fractal flower I meant to post. This image is a rectangular Julia set plot, rendered with such dramatic height changes that it bunches up and doesn't look rectangular any more. Then the camera is placed so close to the image that the perspective distortion makes it look like it radiates from the center:
(http://www.pbase.com/duncanc/image/98932880/original.jpg)

The effect is best if the plot does NOT extend to the edge of the screen. This one works quite well. Sometimes, though, the resulting plot still looks rectangular. I've thought about adding an option to render a circular 2D plot as the basis of one of these 3D flowers, but my code is very biased towards rectangular plots. The array of pixels is a rectangular array, and all possible values but 0 are a legal iteration value. I use zero for "not yet calculated". I'd need to think about how to represent a circular plot.


Regards,

Duncan C

I like this one too. Very cool effect. At first, it did remind me of that style of so-called "fractal art" where an image of a Julia set or some other fractal is just layered on top of a clearly non-fractal photograph, but on closer inspection, this is clearly all fractal with some interesting perspective distortion. Thanks for the explanation of how you created it.

How long does it take to render these images? Is it feasible to make an animation?

It's a pure Julia set, with (massaged) height map data used to render it in 3D. It's then rendered in 3D using a perspective projection in OpenGL.


Rendering times vary wildly depending on the plot and it's size. The flower image renders pretty quickly. To get a screen resolution image I only need to calculate about 800x800 points, and the average number of iterations is around 875 on this plot. I can create this 2D plot in a little less than 5 seconds. The 3D render takes less than 1 second.

The first image in this thread is big, to get the best resolution. The source 2D plot is 2000x2000 pixels. It takes about a 34 seconds to render in 2D. The 3D rendering takes about 3.5 seconds at that size.

2000x2000 pixels is probably overkill for screen display, since that creates polygons that are less than a pixel on each side when the 3D image is rendered at about 1100x800 as it is in first image. 1000x1000 would probably be fine. That smaller size plots the 2D data in about 7.5 seconds, and the 3D render in about 1 second.

Manipulating a 3D image of the 1000x1000 plot on screen is pretty smooth. It's probably giving me 20 fps or so, judging by how smooth it looks.

So animation would be feasible, but not in real time. Generating a high resolution animation would be an overnight affair at least. Figure 5-10 seconds/frame or so for HD quality.

I created a 13 inch x 19 inch print of that first image, and that is quite slow. Creating the 2D data (4000x4000 pixels) takes about 107 seconds, and the 3D render to disk (at 5700 x 3900 pixels) takes about 27 seconds.

Wonderful Duncan - all my compliments :-)))
Margit

Love the smooth and subtle coloring, and intricate detail on this one.

Yet another one I want to zoom into...