User Guide
GNU Image Manipulation Program
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15.12.3.4 Displacement Calculation
The following section will show you how to calculate the amount of displacement, if you are interested in these details. If you
don’t want to know it, you can safely omit this section.
The overview example showed the X displacement using a coefficient of 30.0: 19, 8, 4, or 15 pixels, depending on the grey level
of the displacement map’s color.
Why just these amounts? That’s easy:
30.0 * (I - 127.5) / 127.5 = D If you check these equations, you will notice that the values they give are not exactly the results
we retained in the example (using non-integers, that’s not surprising). So, were the results rounded to the nearest integer and
then the pixels were displaced by a whole-numbered amount? No. Every pixel is displaced exactly by the calculated amount; a
‘displacement by a fractional amount’ is realized by interpolation. A closer look at the example image will show it:
Figure 15.201: A closer look at the displacement example
A small area zoomed in by 800 percent.
The displacement causes small (one pixel wide) areas of intermediate colors at the edges of plain color areas. E.g., the black area
(zoomed in image) is caused by a displacement of -4.12, so the intermediate color is 12% black and 88% gold.
So if you select a displacement coefficient of 30.01 instead of 30.00, you will indeed get a different image, although you won’t
see the difference, of course.
15.12.4 Fractal Trace
15.12.4.1 Overview
This filter transforms the image with the Mandelbrot fractal: it maps the image to the fractal.
You get to this filter via the Image menu through Filters → Map → Fractal trace