So far, this investigation has been about the swirling patterns
produced by moving tines through simple patterns of paint. It has been
computationally convenient to make displacements dependent only on
distances perpendicular to those displacements.
Some marbled designs look as though they are images of a marbled
fabric which has been rippled or gathered.
Regina St. John of Chena River Marblers explained that these
threedimensional effects are achieved by shifting the paper while
lifting it from the paint bath.
The curved fan to the right recapitulates the design from the end of
the first chapter.
 50 10 50
 { /idx exch def
 270 idx sub 30 idx 2 mul add [ 270 idx 3 mul sub ] Circledeformation
 } for
Wiggling the paper sidetoside while lifting it out produces the
expected wiggled design; such sinusoidal distortions were used in the
production of the bouquet patterns.
 50 10 50
 { /idx exch def
 270 idx sub 30 idx 2 mul add [ 270 idx 3 mul sub ] Circledeformation
 } for
 /y exch def /x exch def
 y 7 mul sin 6 mul x add y
Wiggling the paper in the direction of lift stretches and squeezes the
marbled patterns. Unlike the sidetoside wiggle, the excursions must
be limited, lest they overtake themselves and create a fold. A folded
pattern would not be capable of being rasterrendered.
 /y exch def /x exch def
 y 7 mul sin 6 mul y add x exch
Wiggling the paper diagonally, the pattern looks as though it is
flowing down stairs or clapboards. Notice that these horizontal jags
cannot be produced by tine movements. A tine traversing a paint band
bends both sides to the same direction. But here the stretched
horizontal displacements are in opposite directions.
 /y exch def /x exch def
 y 7 mul sin 6 mul dup x add exch y add
Wiggling the virtual paper so violently that it overlaps itself
produces edges that seem to hook under.
 /y exch def /x exch def
 y 7 mul sin 14 mul dup x add exch y add
What if, instead of just wiggling, the paper made a circular motion
while being lifted? The result is striking, looking like paints flowing
over a series of rollers.
 /y exch def /x exch def
 y 7 mul dup sin 6 mul x add exch cos 6 mul y add
If both axes drive the perturbations, it gives the diagonal pattern a
softer appearance. The pattern looks as though it is flowing over
corrugated sheeting.
 /y exch def /x exch def
 y x sub 5 mul sin 6 mul x add y
If both axes drive circular perturbations, the pattern looks as though
it is flowing over rollers or a series of cylindrical troughs.



y x sub 5 mul dup sin 6 mul x add exch cos 6 mul y add
 x y sub 5 mul dup sin 6 mul x add exch cos 6 mul y add

Rasterrendering the diagonal pattern would involve inverting the
vector function
[x + 6 sin(5 (y  x)),
y + 6 sin(5 (y  x))].
But to first order, we can try rasterrendering with
[x + 6 sin(5 (x  y)),
y + 6 sin(5 (x  y))].
With the squeezing and stretching less crisp than above, the
threedimensional effect is not as strong; but it has a more organic
look, which is interesting in its own right.
Some of the threedimensional effect of physical marbling comes from
the stretched regions being lighter in color than the squeezed
regions. That would be difficult to produce using contourrendering
in PostScript  but is simple to add to rasterrendering.
Given that the patterns being stretched and squeezed are not straight
to begin with, and given that shading can be very suggestive of
nonplanarity, just combining an orthogonal wiggle with shading
enables practical transfer effects for rasterrendering.
The next chapter investigates paint drop patterns.
Copyright © 2006 Aubrey Jaffer
I am a guest and not a member of the MIT Computer Science and Artificial Intelligence Laboratory.
My actions and comments do not reflect in any way on MIT.

  Topological Computer Graphics

 agj @ alum.mit.edu
 Go Figure!
