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The IFS equation (1/φ)^D + (1/φ²)^D = 1 has unique solution D = 1. Proved by φ+1 = φ² and strict monotonicity of g(D). Under the open set condition, Hausdorff dimension equals similarity dimension.
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Title CCFU Proof 8 — Fractal Similarity Dimension D = 1 for φ-Branching Tree
The IFS equation (1/φ)^D + (1/φ²)^D = 1 has unique solution D = 1. Proved by φ+1 = φ² and strict monotonicity of g(D). Under the open set condition, Hausdorff dimension equals similarity dimension.
Work type Research papers, Thesis, Lecture notes
Tags similarity dimension, proof, mathematics, ccfu, golden ratio, ifs, fractal, pythagoras tree
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Identifier 2605165670143
Entry date May 16, 2026, 12:12 AM UTC
License All rights reserved
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Author 100.00 %. Holder Captain Cookie Face Universe. Date May 16, 2026.
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