Learning Reduced Order Dynamics via Geometric Representations
Imran Nasim, Melanie Weber
SCML 2024
Mandelbrot's fractal geometry provides both a description and a mathematical model for many of the seemingly complex shapes found in nature. Such shapes often possess a remarkable invariance under changes of magnification. This statistical self-similarity may be characterized by a fractal dimension D, a number that agrees with our intuitive notion of dimension but need not be an integer. A brief mathematical characterization of random fractals is presented with emphasis on variations of Mandelbrot’s fractional Brownian motion. The important concepts of fractal dimension and exact and statisical self-similarity and self-affinity will be reviewed. The various methods and difficulties of estimating the fractal dimension and lacunarity from experimental images or point sets are summarized. © 1986 IOP Publishing Ltd.
Imran Nasim, Melanie Weber
SCML 2024
R.D. Murphy, R.O. Watts
Journal of Low Temperature Physics
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Journal of Crystal Growth
Shu-Jen Han, Dharmendar Reddy, et al.
ACS Nano