Mathematical and Physical Intuition
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March 3, 2026
Sequence Pendulum Wave — Switching Sequences to Observe Position and Periodicity
This Desmos-based “pendulum-wave-like” visualization maps different number sequences into a rotating, connected-point pattern. By switching the active sequence and comparing the same snapshot (e.g., a = 5.5), you can observe how motifs and alignment periods change across primes, odds, Fibonacci, Lucas, composites, and integers.
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March 2, 2026
Dolphin Fractal — A Mandelbrot-Derived Transformation with Absolute-Value Folding
This work creates a new fractal by transforming a Mandelbrot-style iteration in the real plane.
By replacing the x-squared term with a linear x term (while keeping y-squared) and applying a minus absolute-value fold to the y-component, the global silhouette resembles a downward-swimming dolphin, while deep zooms reveal persistent stripe-like structures.
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November 17, 2025
Mandelbrot and Julia Set Parameter Explorer — Dynamic Fractal Simulation and Fibonacci Structures
This Desmos-based exploration turns Mandelbrot and Julia set parameters into movable points, revealing convergence, divergence, Julia connectivity, and Fibonacci-related bulb structures along the boundary.
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October 8, 2025
3D Visualization of Julia Set — Dimensional Folding and Structural Analysis
This work explores the idea that if the Mandelbrot set can be shown in 3D, the Julia set can too.
Using Desmos 3D and a folded complex–quaternion structure, Reiji manually built iterative mappings to visualize the Julia set’s three-dimensional form.
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May 25, 2025
Wave Decay and Considerations Through Limits
This record explores the phenomenon of wave decay from a mathematical perspective. While watching ripples in a bathtub, Reiji began pondering: “What happens to a wave as time approaches infinity?” From this question, he analyzed...