First page



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(15 frames/sec.; each frame is 147 iteration steps Totals: 1260 frames; 185220 iteration steps (92,610 tu))

Parameters: F=0.0600, k=0.0609.

Gray-Scott reaction diffusion system, with parameters F=0.0600 and k=0.0609. This movie demonstrates the immunity of the "U-shaped moving pattern" to systematic random noise.

At each frame (which is 73.5 dimensionless time units) the U and V values at each grid point are altered by a random amount. Beginning at about 3 seconds into the movie, the noise begins at a magnitude of 1.0e-3. Each 10 seconds (11000 dimensionless time units in the simulation) this noise amplitude is doubled. Near the end of the movie the noise is so strong that the U-shaped patterns begin to be destroyed. The noise amplitude is brought back down to 1.0e-3 for a few seconds to show that the remaining U-shape is capable of recovering.

More info at http://mrob.com/pub/comp/xmorphia



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(15 frames/sec.; each frame is 159 iteration steps Totals: 1801 frames; 286359 iteration steps (143,179 tu))

Parameters: F=0.0620, k=0.0610.

Original website movie for F=0.062, k=0.061

This led to my investigation of the areas immediately to the left, eventually leading to all the uskate world phenomena at F=0.06, k=0.0609.



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(15 frames/sec.; each frame is 30 iteration steps Totals: 1801 frames; 54030 iteration steps (27,015 tu))

Parameters: F=0.0180, k=0.0570.

Solitons in "mitosis", maintaining a ring-like shape through to the 16-cell stage.



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(15 frames/sec.; each frame is 521 iteration steps Totals: 1801 frames; 938321 iteration steps (469,160 tu))

Parameters: F=0.0620, k=0.0609.

Discovery of the "u-skate" phenomenon, from 2009 March 23, re-rendered into standard colors. (Compare to the original)



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(15 frames/sec.; each frame is 1333 iteration steps Totals: 600 frames; 799800 iteration steps (399,900 tu))

Parameters: F=0.0600, k=0.0609.

Complex interaction involving the common U-shaped moving pattern, a negative stripe with annulus, and a triangular group of 6 negatons.

The U-shaped object survives the first interaction, causing the triangular group to shift significantly in the process. On the second interaction the U is a bit closer to the annulus and is annihilated when it comes into contact with the triangle.

The groups of dots at the top of the image are also moving, but much more slowly — see following video.

Simulation speed is 10,000 dimensionless time units per second.



(watch this on YouTube)

(15 frames/sec.; each frame is 13333 iteration steps Totals: 1801 frames; 24012733 iteration steps (12,006,366 tu))

Parameters: F=0.0600, k=0.0609.

Several slow-moving patterns made of dots: the three-dot and five-dot patterns move to the right; the four-dot patterns rotate (in opposite directions).

The large pattern to the lower right shifts into a symmetrical form, which then rotates while retaining its symmetry.

For reference, two U-shaped moving patterns are set on a collision course in the lower-left section. Their speed helps illustrate how slow the other moving patterns are by comparison.

When the U-patterns collide, the result is a 4-dot pattern that is in an unstable equilibrium configuration: any very slight perturbation will make them shift into a different (and stable) 4-dot arrangement. This shift is not seen here only because roundoff error prevents the initial (very slow) beginning of this transition from being properly simulated.

Simulation speed is 100,000 dimensionless time units per second.



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(15 frames/sec.; each frame is 100 iteration steps Totals: 1801 frames; 180100 iteration steps (90,050 tu))

Parameters: F=0.0600, k=0.0609.

This is the stable moving pattern "Daedalus" (named after Project Daedalus because of its resemblance to that spaceship, see the Wikipedia article) being subjected to noise immunity testing. This pattern moves in the direction of the five dots, at a rate of one dimensionless length unit per 3.9×106 dimensionless time units.

Simulation rate in this animation: 750 dimensionless time units per second.



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(15 frames/sec.; each frame is 10 iteration steps Totals: 1801 frames; 18010 iteration steps (9,005 tu))

Parameters: F=0.0230, k=0.0525.

One-dimensional traveling pulses that "reflect" off each other when they meet.


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