Gray-Scott Nomenclature Glossary

This glossary is incomplete. Contact me with any specific requests for additions or corrections.

blue : The color generally used for areas of high u values. In monochome images the high-u regions are a darker gray or black. The blue-red color scheme was used by Pearson [1], replicating the pH indicator bromothymol blue used in physical experiments of e.g. Lee et al. [2]. See also red.

branch : In general, any linear feature that has a tip and which is connected at its other end to another linear feature.

branch point : a place at which three (or rarely, more than three) linear features come together.

branching structure : any pattern(s) involving linear features linked by branch points.

clover : A closed loop with roughly 4-fold symmetry, including four segments of concave curvature and four (larger) segments of convex curvature. For an example, see the loop in the upper-right of (F=0.058, k=0.063). See also (F=0.046, k=0.063).

Many parameter values that support clovers also support Hilbert loops.

drift : Describes the tendency of type nu solitons to repel one another, at a rate that diminishes exponentially with distance.

east : In parameter space, the direction in which the parameter k increases.

grain : An region containing a locally regular pattern, contrasted with a neighboring region in which the pattern is different. The grains meet at a boundary.

grain boundary : The boundary between two grains.

Hilbert loop : A closed loop similar to a clover, that grows while developing gradually increasing complexity. See (F=0.062, k=0.063) for an example.

A "true" Hilbert loop will grow indefinitely without ever developing branches; however most parameter values produce loops that produce branches when space becomes tight.

junction : a place where three grains meet.

mitosis : A pattern-evolution process in which a single type lambda soliton splits into two. The process repeats as available space permits.

negative : Used to describe name features that resemble another more common feature but with high-u areas exchanged for low-u areas and vice-versa. For example, compare the network of linked loops or bubbles at (F=0.098, k=0.057) to a similar network of linked negative loops at (F=0.098, k=0.055).

negative pattern : In general, any pattern that consists mostly of high-u ("blue") space with occasional low-u ("red") features.

negative worm, negative stripe, etc. : a low-u worm surrounded by high-u space. For example, see (F=0.070, k=0.061).

negative soliton : a negaton.

negaton : A region of red (or more generally, relatively lower-u values) surrounded by blue and which resembles an inverted soliton. A true negaton is a self-sustaining feature with perfect symmetry (in absence of influence of neighboring features); such negatons can be seen at (F=0.046, k=0.0594) and at (F=0.062, k=0.061). In the more general sense, a "negaton" can be any generally small and circular red region surrounded by blue; for example see (F=0.094, k=0.057) and note the small round spots that eventually grow into larger and non-circular shapes.

north : In parameter space, the direction in which the parameter F increases.

red : The color generally used for areas of low u values. In my images it is usually more "pink" than red, and in monochome images it is a lighter gray or white. See blue for origin.

seed : Can refer to any small pattern that develops into something larger and more complex. I am using the term only when referring to a spiral seed.

soliton : A sole, self-sufficient and stable (asymtotically unchanging) island of locally low u surrounded by locally higher u. For example, see (F=0.054, k=0.067).

south : In parameter space, the direction in which the parameter F decreases.

spiral : This term is used specifically to refer to the self-sustaining structures, reminiscent of the B-Z (Belousov- Zhabotinsky) reaction in a Petri dish, that are found at lower F values such as (F=0.006, k=0.031) and (F=0.014, k=0.045).

spiral seed : see seed.

tip : The rounded end of a linear feature. For example, worms have two tips.

west : In parameter space, the direction in which the parameter k decreases.

worm : A straight or curved but (generally roughly linear) "soliton" with two rounded ends and no branching structure. For examples, see (F=0.082, k=0.061) and (F=0.086, k=0.061). The structure is like a soliton in that the linear part does not narrow or widen, but is unstable at the ends (which either grow, as seen at (F=0.082, k=0.061), or shrink as at (F=0.086, k=0.061)).

XMorphia : The name of a website created by Roy Wlliams in 1994, based on the Pearson paper [1] using supercomputer resources at Caltech. It is preserved by archive.org; view its December 1998 incarnation here. XMorphia featured a clickable parameter-space image, which appears in a greatly expanded form on my site.

References

[1] J. Pearson, Complex patterns in a simple system, Science 261 (1993) 189-192.

[2] K. J. Lee, W. D. McCormick, H. L. Swinney, and J. E. Pearson, Experimental observation of self-replicating spots in a reaction-diffusion system, Nature 369 (1994) 215-218.

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