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Author Topic: Creating 3D plots in FractalWorks  (Read 2603 times)
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Duncan C
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« on: April 30, 2009, 04:29:48 AM »

One of the more interesting features of FractalWorks is it's ability to render your fractal images in 3D. This is not a 3D "filter" that creates a 3D look - rather, every pixel in your fractal is assigned a height value, and the program uses the OpenGL graphics language to render the fractal as true 3D object, which is then lit using directional lighting.

FractalWorks can create 3D plots using 3 different types of data. It can use integer iteration values to create height values. This is a "quick and dirty" approach that is of limited value. It's quick and dirty because integer iteration values are relatively fast to calculate, and FractalWorks can take a number of shortcuts when it does not have to calculate fractional iteration values or distance estimates (mentioned below.) When you use integer iteration values to create a 3D image, the 3D plot has distinct "stairsteps" as the integer iteration value changes. Here is a sample 3D plot created using integer iteration values:


(Click on the image to see a larger version that includes a link you can use to recreate the plot using your copy of FractalWorks)


The second option is to request that fractalWorks generate fractional iteration values for each pixel. These values are very much like integer iteration values, except that they change smoothly, without distinct jumps from one integer value to the next. You request  that FractalWorks calculate fractional iteration values in the new plot dialog. Here is a sample 3D image created using fractional iteration values:


(Click on the image to see a larger version that includes a link you can use to recreate the plot using your copy of FractalWorks)

Note that this plot has basically the same shape as the previous plot, but without the "stair-step" effect. Also be aware that your plot should include fractional iteration data if you want your plot's colors to have smooth transitions without jumps in color like in the example above.

Here is the plot above using fractional iteration values to smooth color transitions:


(Click on the image to see a larger version that includes a link you can use to recreate the plot using your copy of FractalWorks)

The third option is to use distance estimate data to generate height values for every pixel. Distance estimates are a mathematical formula that lets the program figure out how far any pixel in the plot is from the nearest Mandelbrot set (or Julia set) point. This option creates the most interesting 3D shapes. You also request that Fractalworks generate distance estimate data in the new plot dialog. Here is what the sample image looks like using distance estimates to calculate the height of pixels in the plot:


(Click on the image to see a larger version that includes a link you can use to recreate the plot using your copy of FractalWorks)

FractalWorks is written to use distance estimate data for 3D plots if it's available. If the plot does not include distance estimate data, FractalWorks will use Fractional iteration values instead. If neither of those is available, it will use integer iteration value to create it's 3D plots.

Generally, you will want to use distance estimates to create your 3D plots. Distance Estimate data seems to give the most interesting shape to 3D plots. Nearly all the 3D Fractalworks  you see in my PBase gallery or in the flickr FractalWorks gallery are created using Distance Estimate data.

If you want to experiment, find a 2D plot that looks interesting. Then select "get file info" and look for the following lines of information:

Plot uses DE:   Yes
Plot uses fractaional iterations:   Yes

If the line "Plot uses DE" is followed by "No", the plot does not include distance estimate data. In that case you should select "new plot" from the file menu, and check the box at the bottom of the new plot dialog labeled "Calculate Distance Estimates." Then press return to recalculate the plot and calculate distance estimate data.

Once you have a plot that includes distance estimate data, select "Show 3D View" from the view menu. This will bring up a second view of the fractal, this time rendered as a 3D object.

You can then adjust various settings to change the look of the plot. The "Plot height" setting changes the total height of the plot. At a value of 1, the plot will be as tall as it's longest 2D dimension. (If the 2D plot is square, the plot will fill the shape of a cube.)

Smaller values for "plot height" make the image height lower. A value of .01 makes the plot almost completely flat, like a 2D plot.

The meaning of the "peak steepness" value is a little harder to explain. Large "peak steepness" values make the steepest part of the plot near the peaks. Small values for "Peak steepness" flatten out the top of the plot and shift the steepest slope to the lowest height values.

Logged

Regards,

Duncan C
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