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Space-time generation of high intensity patterns using growth-interaction processes

Renshaw, E. and Comas, C. (2009) Space-time generation of high intensity patterns using growth-interaction processes. Statistics and Computing, 19 (4). pp. 423-437.

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Abstract

We describe a novel spatial-temporal algorithm for generating packing structures of disks and spheres, which not only incorporates all the attractive features of existing algorithms but is also more flexible in defining spatial interactions and other control parameters. The advantage of this approach lies in the ability of marks to exploit to best advantage the space available to them by changing their size in response to the interaction pressure of their neighbours. Allowing particles to move in response to such pressure results in high-intensity packing. Indeed, since particles may temporarily overlap, even under hard-packing scenarios, they possess a greater potential for rearranging themselves, and thereby creating even higher packing intensities than exist under other strategies. Non-overlapping pattern structures are achieved simply by allowing the process to 'burn-out' at the end of its development period. A variety of different growth-interaction regimes are explored, both symmetric and asymmetric, and the convergence issues that they raise are examined. We conjecture that not only may this algorithm be easily generalised to cover a large variety of situations across a wide range of disciplines, but that appropriately targeted generalisations may well include established packing algorithms as special cases.