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Maximizing Circular Tiles On Fractals: A First Step To Optimization In Fractals

Author

Listed:
  • CARMEN GARCÃ A-MIGUEL

    (Universidad Politécnica de Madrid, Spain)

  • JESÚS SAN MARTà N

    (Universidad Politécnica de Madrid, Spain)

Abstract

Fractal covering with non-overlapping circular tiles follows a power law, when the circular tiles cover a preset mass of the fractal and their centers are chosen randomly and successively. Once the fractal has been saturated with the circular tiles, the tile size frequency distribution follows a parabolic fractal law. Distribution parameters are related and depend only on fractal dimension and fixed fractal mass of tiles. The distribution of the tiles can be used to optimize the allocation and/or exploitation of resources on fractals.

Suggested Citation

  • Carmen Garcã A-Miguel & Jesãšs San Martã N, 2021. "Maximizing Circular Tiles On Fractals: A First Step To Optimization In Fractals," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-17, September.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:06:n:s0218348x2150167x
    DOI: 10.1142/S0218348X2150167X
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