Hausdorff Dimension of the Brownian Earthworm (WXML Winter 2017 Report)
Clayton Barnes, Krzysztof Burdzy, Alex Forney, Zach Dingels, Xiyi Yan,, and Ran Zhao
TL;DR
This paper presents simulations indicating that the Hausdorff dimension of the Brownian earthworm's trace exceeds 1.5, supporting a conjecture about its fractal complexity.
Contribution
It provides computational evidence for the conjecture that the Hausdorff dimension of the Brownian earthworm's trace is greater than 3/2.
Findings
Simulations support the conjecture that the dimension exceeds 3/2.
Evidence suggests the trace has a fractal structure.
Supports theoretical predictions about Brownian paths.
Abstract
Simulations support the conjecture that the dimension of the trace of Brownian earthworm is strictly greater than 3/2.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Ecosystem dynamics and resilience · Complex Systems and Time Series Analysis