Auxiliary Gray-Scott Images and Movies
This is a collection of Gray-Scott images and movies that serve as a supplement to the main exhibit. Some of these are produced with parameters that are within the area covered by the main exhibit, but are "in between" the standard grid points. Others are at standard grid points but were produced with special starting patterns.
The parameters (F=0.098, k=0.056)
These parameters (and nearby values) support a very wide range of behaviours and patterns. Although the final states are similar, behaviour varies greatly depending on the type of initial pattern (mainly red or mainly blue) and precise details of its configuration.
(15 frames/sec.; each frame is 1200 iteration steps. Totals: 1801 frames; 2161200 iteration steps (1,080,600 tu)
Parameters: F=0.0980, k=0.0560.
Blue spots grow into ovals, which readily elongate into slowly-growing "wide worms" (upper-right) which maintain a fixed spacing when traveling side by side (e.g. the pair in upper-left; and at 1:00 note the worm in the lower-left bends to the left to keep its distance from the other two). When pressed from the side (center of screen at 1:28) these wide worms narrow, and the narrowing travels quickly to both ends, but the ends themselves remain wide. If a worm tip is constrained it becomes narrow (watch center at 1:44) and the narrow worm-tip grows more quickly. Ultimately the entire space is filled with the narrow type of worm.
(old video: CO2fl9nhcpQ was encoded poorly.)
(15 frames/sec.; each frame is 2000 iteration steps Totals: 4001 frames; 8002000 iteration steps (4,001,000 tu))
Parameters: F=0.0980, k=0.0560.
A large blue area will grow from the "corners", and the center also steadily grows. The corners generally grow faster; the three seen here are like the "wide worms" above. As above, they can bend (0:30 - 0:45) but when poked from the side, transform into normal-width worms (lower-left, 0:52). At 1:06, one of the tips narrows and then begins lengthening much more quickly; this soon precipitates narrowing of the other features and the large blue area shrinks to nearly nothing (1:25 - 1:50). A fourth wide-worm arises at 2:00, and the space eventually becomes filled with parallel stripes. Worms can shorten and disappear, as seen from 3:10-3:22. The drifting motion seen at the end of the video continues indefinitely.
(old video: 5dWdPm94iyI was encoded poorly.)
(15 frames/sec.; each frame is 2000 iteration steps Totals: 3958 frames; 7916000 iteration steps (3,958,000 tu))
Parameters: F=0.0980, k=0.0560.
In a mostly blue background, most red spots become stable negatons. However, any sufficiently convoluted red area, or an area containing a blue "island", results in worm tips. These grow steadily, but twist and turn in response to the negatons and other obstacles. The red boundaries naintain a fairly constant width, and negatons expand a bit when a red boundary touches them (right of center, 0:25-0:35). Negatons will disappear if pressured (near center, 0:51).
(old video: P8pdhVBrsZQ was encoded poorly.)
Parameters near Uskate World
Here are some movies showing what happens at values of F and k close to uskate world.
(Accelerating time-lapse; speed doubles every 9 seconds. Totals: 2549 frames; 4.89×109 iteration steps (2.44×109 tu)
Parameters: F=0.0600, k=0.0613.
Accelerating time-lapse; speed doubles every 9 seconds. Space quickly fills with concentric loops and negatons; the loops coalesce and lengthen, becoming generally straighter and more parallel. Worm tips grow until something makes them run into a wall, then another worm tip grows in another direction (see 0:50 - 1:20). This process seems to continue indefinitely: this time-lapse shows 2.44×109 tu of evolution.
(old video: XPndrF4-atQ was encoded poorly.)
Uskate World in One Dimension
Stable moving patterns also exist in one-dimensional Gray-Scott systems, and at the same F and k parameter values as in the 2-D system.
(15 frames/sec.; each frame is 10000000 iteration steps. Totals: 1801 frames; 1.8×1010 iteration steps (9,005,000,000 tu))
Parameters: F=0.0600, k=0.0609.
This is a one-dimensional simulation; the colored bar shows the pattern in the same colour-scheme as my 2-D movies; and the black and white lines show the levels of u and v respectively. These F and k parameter values support bound groups of negative solitons; this particular pattern (called "1011") drifts to the right very slowly.
(old video: DkukL5o2dwo was encoded poorly.)
(Accelerating time-lapse; speed doubles every 9 seconds. Totals: 1717 frames; 77263730.9862835 iteration steps (38,631,865 tu))
Parameters: F=0.1020, k=0.0550.
Accelerating time-lapse; speed doubles every 9.25 seconds. Solitons and a few worms that grow to fill the space. The worms corral the solitons but homotopy is preserved. The orientation of the worm-tips drives the overall direction of movement of the pattern; when space is full even the down-facing worm tips are forced to reverse direction. (as seen at 1:30-1:40)
This behavior is typical of many parameters that support both worms and solitons, and where the surface tension is positive.
(old video: GG4mPeHV8Bo was encoded poorly.)
(Accelerating time-lapse; speed doubles every 9 seconds. Totals: 2201 frames; 863673443.735979 iteration steps (431,836,721 tu))
Parameters: F=0.1100, k=0.0523.
Accelerating time-lapse; speed doubles every 9 seconds. Totals: 2201 frames; 863673443.735979 iteration steps (431,836,721 tu)
Time-lapse of the system seen at (F=0.110,k=0.051)
(15 frames/sec.; each frame is 147 iteration steps Totals: 208 frames; 30576 iteration steps (15,288 tu))
Parameters: F=0.0600, k=0.0620.
Turing pattern evolving from low-level random noise.
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This page was written in the "embarrassingly readable" markup language RHTF, and some sections were last updated on 2010 Dec 29.
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