Semester of Graduation
Master of Natural Sciences (MNS)
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 ∈ ℕ) for 𝑇 = 𝑇1 ∪ 𝑇2 ∪ 𝑇3, where 𝑇1(𝑧) = 𝑟𝑧, 𝑇2(𝑧) = 𝑟𝑧 + 𝑏, and 𝑇3(𝑧) = 𝑟𝑧 - 𝑏, and 𝑟 = 𝑒𝑖π/3.
Kelly, William H. III, "Fractal Like Snowflakes Generated by Non-Contractive Function Systems" (2022). LSU Master's Theses. 5690.