Semester of Graduation

Fall 2022

Degree

Master of Natural Sciences (MNS)

Document Type

Thesis

Abstract

At the heart of this thesis is the examination of a non-contractive iterative function system T on the Hausdorff metric space of all compact subset of ℝ . Despite the absence of an 2 attracting fixed point, an examination reveals the appearance of fractal-like shapes (snowflakes) when applying the Barnsley’ random walk method to study the iterative sequence 𝑇n(0) (𝑛 ∈ β„•) for 𝑇 = 𝑇1 βˆͺ 𝑇2 βˆͺ 𝑇3, where 𝑇1(𝑧) = π‘Ÿπ‘§, 𝑇2(𝑧) = π‘Ÿπ‘§ + 𝑏, and 𝑇3(𝑧) = π‘Ÿπ‘§ - 𝑏, and π‘Ÿ = 𝑒𝑖π/3.

Date

11-3-2022

Committee Chair

Neubrander, Frank

Included in

Mathematics Commons

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