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Plane DLA is not self-similar; is it a fractal that becomes increasingly compact as it grows?

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  • Mandelbrot, Benoit B.

Abstract

Using two new methods of geometric analysis, this paper establishes that DLA clusters are definitely not self-similar. Compared to small clusters, the morphology of large clusters (of sizes up to 30 million particles) can be characterized, both visually and quantitatively, as being far more “compact” or less “lancunar”. Qualitatively, the number of “arms” increases during growth. The evidence does not exclude that the cluster remains fractal, and that its fractal dimension remains constant; however, new pitfalls in the estimation of D are revealed. The gradual change in the morphology of DLA opens the possibility that there is continuity between the standard morphology observed for small to medium computer generated DLA clusters and the compact morphology observed in many actual physical phenomena.

Suggested Citation

  • Mandelbrot, Benoit B., 1992. "Plane DLA is not self-similar; is it a fractal that becomes increasingly compact as it grows?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 191(1), pages 95-107.
    • Handle: RePEc:eee:phsmap:v:191:y:1992:i:1:p:95-107
    DOI: 10.1016/0378-4371(92)90511-N
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