The Fractal Dimension of Random Sets Generated from Multitype Galton-Watson Trees
This research paper presents a novel method for calculating the Hausdorff and box dimensions of random fractal sets generated using multitype Galton-Watson trees, demonstrating that these dimensions coincide and can be explicitly determined using the spectral radius of the associated reproduction matrix.
Fractal Dimension: Challenges and Pitfalls in Estimation
While widely used, calculating fractal dimension (specifically Sevcik's dimension, DS) from waveforms presents challenges due to the impact of data uncertainty, convergence speed, and the limitations of existing estimation methods.
Box Dimension of Fractal Interpolation Functions on Attractors: A Study with Non-Uniform Interpolation Points and Non-Affine Maps
This research paper investigates the box dimension of fractal interpolation functions (FIFs) defined on attractors, particularly focusing on scenarios with non-uniformly spaced interpolation points and non-affine maps in the underlying iterated function system (IFS).
Sphractal: Estimating Fractal Dimension of Surfaces from Atomic Coordinates
Fractal dimension estimation of atomistic surfaces using box-counting algorithms.
Sphractal: Estimating Fractal Dimension of Surfaces from Atomic Coordinates
Estimating fractal dimensions of atomistic surfaces using box-counting algorithms.
Sphractal: Estimating Fractal Dimension of Surfaces from Atomic Coordinates
The author proposes methods to estimate the fractal dimension of surfaces composed of spheres using voxelised point clouds or mathematically precise surfaces, demonstrated through Sphractal.
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