The most complex color patterns take the form of what I call Chromatized Transformations. They draw on some of the simpler techniques (see Clines and Chromatized Patterns), but add new layers of complexity to create visually interesting variations on the patterns.

The examples below employ three standard tiles, the Roseate, the Screen, and the Ornate:

Roseate

Screen

Ornate

A standard linear horizontal cline using the Ornate tile produces this transformation:

Also using the Ornate tile, the core piece of code below is executed to create a cosine-based transformation that color-shifts the pattern through about 25% of the spectrum, and then brings it back in a smooth curve to the original:

For i = 0 To ImageWidth - 1
    Theta = i / ImageWidth * TwoPi - Pi
    HorizCoeff = (Cos(Theta) + 1) / 2
    For j = 0 To ImageHeight - 1
        Color2 = PickOffChroma(Template, i Mod TemplateWidth, j)
        Color3 = SpecColor(RedHue + RedHueShift * HorizCoeff, RedBright + RedBrightShift * HorizCoeff, RedVivid).Color
        Color4 = SpecColor(GreenHue + GreenHueShift * HorizCoeff, GreenBright + GreenBrightShift * HorizCoeff, GreenVivid).Color
        Color5 = SpecColor(BlueHue + BlueHueShift * HorizCoeff, BlueBright + BlueBrightShift * HorizCoeff, BlueVivid).Color
        Color1 = ThreeColor(Color2, Color3, Color4, Color5)
        Output.PSet (i, j), Color1.Value
    Next j
Next i

This is the final result:

The patterns below use the Roseate and Screen tiles in varying combinations.

First we have a plain pattern with no clines or other transformations, based on the Roseate tile:

Below is an example of what can be done with the same tile, using the same basic colors. This one, however, features transformations in hue, brightness, and vividness, with two distinct schemas of variation, one horizontal and the other vertical:

The next variant uses the same color transformations, but the pattern itself also transforms horizontally, beginning with the Roseate tile and merging seamlessly into the Screen tile:

Transformation: clines plus pattern transformation

Finally, additional complexity is achieved by programming distortions of size and orientation into the horizontal and vertical progressions of the component tiles:

Transformation: clines, pattern transformations, and matrix transformation

The above pattern demonstrates the flexibility and sophistication of the visual cortex of the human brain. Nothing remains the same in this image, whether the eye tracks from top to bottom or from left to right. The size, color, relative brightness, and even the component elements metamorphose in both directions. Yet the brain is never in any doubt that there is a consistent pattern involved, and perceives it as such.