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Information modification and particle collisions in distributed computation
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10.1063/1.3486801
/content/aip/journal/chaos/20/3/10.1063/1.3486801
http://aip.metastore.ingenta.com/content/aip/journal/chaos/20/3/10.1063/1.3486801

Figures

Image of FIG. 1.
FIG. 1.

Local information dynamics in rule 54 (35 time steps displayed for 35 cells, time increases down the page for all CA plots). (a) Raw states with “0” in white and “1” in black. All other profiles are discretized into 16 levels with blue for positive values and red for negative. (b) Local active information storage, maximum of 1.07 bits, minimum of −12.27 bits (with negative values concentrated on the and gliders). Local apparent transfer entropy: (c) one cell to the right, maximum of 7.93 bits, minimum of −4.04 bits (with negative values concentrated on the gliders), (d) one cell to the left, maximum of 7.93 bits, minimum of −4.21 bits (with negative values concentrated on the gliders). (e) Local separable information, maximum of 8.40 bits, minimum of −5.27 bits (with areas containing large negative values circled and labelled). (f) Close-up of raw states of rule 54 in collision type A. “x” and “” mark some positions in the and gliders, respectively. Note their point of coincidence in collision type A, with “” marking what initially appears to be the collision point and “o” marking the subsequent information modification as detected using .

Image of FIG. 2.
FIG. 2.

Local information dynamics in rule 110 (55 time steps displayed for 55 cells). (a) Raw states with “0” in white and “1” in black. All other profiles are discretized into 16 levels with blue for positive values and red for negative. (b) Local active information storage, maximum of 1.22 bits, minimum of −9.21 bits (with negative values concentrated on the gliders). Local apparent transfer entropy: (c) one cell to the right, maximum of 9.99 bits, minimum of −5.56 bits, (d) one cell to the left, maximum of 10.43 bits, minimum of −6.01 bits (with negative values visible on the right-moving glider). (e) Local separable information, maximum of 5.47 bits, minimum of −5.20 bits (with the largest negative values labelled, and others visible in the right-moving glider).

Image of FIG. 3.
FIG. 3.

Local information dynamics in rule 18 (67 time steps displayed for 67 cells). (a) Raw states with “0” in white and “1” in black. All other profiles are discretized into 16 levels with blue for positive values and red for negative. (b) Local active information storage, maximum of 1.98 bits, minimum of −9.92 bits (with the largest negative values on the domain walls, and others in locations discussed in Sec. II A). Local apparent transfer entropy: (c) one cell to the right, maximum of 11.90 bits, minimum of −7.44 bits (with negative values where the domain walls move left), (d) one cell to the left, maximum of 11.90 bits, minimum of −7.30 bits (with negative values where the domain walls move right). (e) Local separable information, maximum of 1.98 bits, minimum of −14.37 bits (with the area with the largest negative values circled, and others in locations discussed in Sec. IV C).

Image of FIG. 4.
FIG. 4.

Our expectations for the local information dynamics of storage and transfer for unperturbed gliders (coherent structures) and glider collisions. (a) For unperturbed gliders in channel , we expect the transfer in the direction of glider motion to be positively informative, and indeed more informative than the misinformation conveyed through and . (b) For a collision perturbing a glider moving in the channel , we can no longer expect the transfer in the direction of glider motion to be positively informative at the collision point. We cannot expect the transfer in the direction of the incident glider to be positively informative at the collision point either.

Image of FIG. 5.
FIG. 5.

Separable information for one-dimensional CAs : information gained about the next state of the destination from separately examining each causal information source in the context of the destination’s past . For CAs these causal sources are within the cell range .

Tables

Generic image for table
Table I.

Classification of information modification event types [i.e., with ] in cellular automata using information storage and transfer properties as a secondary tool [after ].

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/content/aip/journal/chaos/20/3/10.1063/1.3486801
2010-09-28
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Information modification and particle collisions in distributed computation
http://aip.metastore.ingenta.com/content/aip/journal/chaos/20/3/10.1063/1.3486801
10.1063/1.3486801
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