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Cellular Automata Simulations for Tensor Field Analysis

This work elaborates on the mechanisms behind cellular automata simulations developed by Robert Alvarez, Dakota Boyd, Hyder Hussain, and Jonathan Martin. It defines randomized NxN domains and generates MxM grids of filters based on an MxM tensor field. The domain is updated through 2D correlation of filter matrices with segments of the full domain, and a smoothing filter is applied for further enhancement. The implementation has undergone multiple versions, with elapsed times recorded for performance assessments, showcasing effectiveness in force filter applications.

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Cellular Automata Simulations for Tensor Field Analysis

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  1. Simulations: Cellular Automata Robert Alvarez, Dakota Boyd, Hyder Hussain, Jonathan Martin

  2. Mechanism • Defines rand() NxN domain. • Generates MxM grid of filters based on an MxM tensor field. • Updates the domain via 2D correlation of the filter matrices with segments of the full domain. • Updates the domain with a smoothing filter

  3. Forces

  4. Forces

  5. Sample Filters Tensor Filter 0 -0.0026 -0.0065 -0.0026 0 0.0026 0 -0.0130 0 0.0026 0.0065 0.0130 0 0.0130 0.0065 0.0026 0 -0.0130 0 0.0026 0 -0.0026 -0.0065 -0.0026 0 Smoothing Filter 0 -0.0150 -0.0117 -0.0150 0 -0.0150 0.0046 0.0371 0.0046 -0.0150 -0.0117 0.0371 0 0.0371 -0.0117 -0.0150 0.0046 0.0371 0.0046 -0.0150 0 -0.0150 -0.0117 -0.0150 0

  6. Implementation of Force Filter

  7. Implementation of Force Filter

  8. Version 1.0 Elapsed time is 5.037525 seconds.

  9. Version 3.0 Elapsed time is 9.191040 seconds.

  10. Version 4.0 Elapsed time is 5.250095 seconds.

  11. Version 5.0 Elapsed time is 5.551649 seconds.

  12. Version 8.0

  13. Version 9.0

  14. Version 10.0

  15. Version 11.0

  16. Version 12.0 Tensor

  17. Version 12.0

  18. Questions? http://us.123rf.com/400wm/400/400/sorad/sorad1103/sorad110300085/9128505-fingerprint-question-mark.jpg

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