Random is OK but no control over your ultimate destiny. So if you feed -tiletex images that have luminous pixels, it will take these to be coefficient settings. The first argument still sets window size, but now -tiletex is using that argument to limit its attention to just a modest sized region around the Zero Pole. The second argument to -tiletex, 0 here, is a common phase angle argument, which should make your head ring just a little bit. -tiletex likes complex numbers in polar form, an alternate notation for picking out points on the complex number plane. Instead of so many increments horizontally, (a), then so many increments vertically (b), the polar form takes the length of a ray (r) and a rotation amount (θ) to pick out a point on the complex number plane. The rotation amount is the phase angle and the length of the ray is the magnitude. This second argument to -tiletex lets it know that we're not furnishing any phase angles, just magnitudes, and every single blessed one of those complex numbers are to have a common phase angle of zero. This lets us just furnish one input image, setting magnitudes.

The three lefthand images are not the literal input. We have magnified a 16×16 pixel region around the Zero Pole and superimposed a grid to help visualize the location of coefficients. If you peak inside of radius_20.png, you will find these pixels clustered around the image center, depicted here just to the right and below the intersection of the crosshairs.

The righthand images are the result of these four coefficients metamorphing into waveforms which then reinforce one another here, but then cancel one another there. Notice that how we distribute coefficients matter. When we favor one quadrant, the pattern becomes strongly diagonal.

Tilable textures are not ends in themselves. Often they go on as pieces in some larger graphic puzzle. In this panel, a low frequency, two channel spatial rendition of a very few spectral coefficients continues its career as a vector field, one exhibiting a full repertoire of shears and whirlpools. 

Some notes on the script: -tiletex has been given only input magnitudes in wavespectral.png, a very few non-zero pixels (coefficients) near the center of the image. The first argument to -tiletex, 20, tells -tiletex to only survey a small square around the Zero Pole. The second argument to -tiletex, 30, sets a common angle of 30° to all the magnitudes found in that window. The third argument to -tiletex, 1, tells it that we are only interested in the real spatial output window. 2 gives us only the imaginary window and 0, the default, provides both.

For the rest of the script, spend some time with -orientation and -warp, We (rather arbitrarily) chose to regard the red and green color components as those of a two dimensional vector, and having made this leap, harnessed -orientation to normalize all of them to unit length. The common purpose for this is to get a fairly direct read on the heading of vectors – their component lengths are the sines and cosines of their heading angles (that is, their orientation). The uncommon purpose is that sign transitions in the original data develop into abrupt creases. They make particularly interesting warp fields. The right hand image in the top row illustrates the results of this enterprise. We apply this green-yellow-red direction field to the face via the -warp command.

It is not difficult to emulate a 1970's era color television set on the fritz, in case the need for such ever arises, which my childhood friend Melvin did for real. A mechanically inclined youngster, he tightened all of the screws in the back of the family color TV set to get rid of a rattle and inadvertently anticipated G'MIC's -warp command by over a quarter century. Alas, he never published. His worldliness was limited at that age. Nobody ever told him about radio frequency circuits either, along with those core adjustment screws on top of the RF coils. But he did make sure that they were pretty darn tight.

Ah. We seem to have digressed.

Almost everything about this animation is the technique on the left repeated, oh, 2,048 times, or there abouts. The bit that is new is the animation of the warp field.

The inside of wavespectral.png, the input image to -tiletex, looks pretty much like the examples in the previous row, those on the left: a bunch of coefficients around the Zero Pole in various colors. In the pipeline that made the 2,048 warp fields for the animation, those coefficients changed color. They were, as engineers like to say, parametrically driven, which is a round-about way of saying they changed color over the length of an interval divided into 2,048 slices, and they changed a little bit for each slice. Since these are spectral coefficients, under Fourier synthesis they morph into waveforms, so as the coefficients change, so change the waveforms. With each increment, they don't wave in quite the same magnitude or phase as before.

The question of how much they change (how fast, what direction) is a matter of taste. In our minds, we had the tentative jerkiness of a color television set with its vertical and horizontal hold circuits very much out of tune (but pretty tight!). For us, the quirkiness of -turbulence, Mode 0, was just the thing, so you should spend some time with that tutorial.

So imagine a -repeat … -done loop iterating over a 2048 × 1 three channel (RGB) image that had been worked over by -turbulence with a radius of about 80 to 128, 6 to 12 octaves, a decay factor of 3 or 4, no differencing and Mode 0, because in mode 0 turbulence makes these abrupt transitions — jerks! — that seem especially apt. Two of these long skinny images, one for magnitude the other for angle, were concocted for each coefficient, three chiral pairs, six coefficients, twelve data sets. On each turn of the repeat loop, we took the indexed colors out of each long skinny image and used it to change the color of its corresponding coefficient. Usually, the colors changed slightly, but sometimes one or another would get a turbulent wack, hence the jerkiness.

That Swiss Army knife of video file manipulators, ffmpeg, generated the 2,048 test frames, basic colorbars and a time counter, something that one can do when defining a filter chain. This footage was then warped (-warp) and composited (-blend, difference,0.5) againt the real output image of -tiletex, giving a ghosty, shadow-like coloring. We added a wisp of mode 0 -noise for that faux film effect.