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The visualization shows a self-squared dragon fractal, a geometric pattern constructed by recursively arranging smaller copies of a dragon curve into a square configuration. It depicts how the classic dragon curve, known for its self-similarity and space-filling properties, transforms at multiple scales, with colors shifting from blue to yellow and line widths thinning at deeper recursion levels. The code uses d3.line and d3.curveBasis to render SVG paths, while custom recursive functions and geometric transformations handle scaling, rotation, and translation. The fractal is generated from an initial curve produced by D3 v7, with level-based hue and opacity styling applied to differentiate each recursive tier.
AI-generated descriptionSelf-Homographic Fractal Near the Peano Limit
This visualization creates a self-homographic fractal that approaches the space-filling property of a Peano curve. The fractal is constructed using recursive application of homographic transformations.
About the Visualization
This fractal uses proper homographic (projective) transformations to create a self-similar pattern that approaches, but never quite reaches, the space-filling property of the Peano curve.
A homographic transformation is a type of transformation that can be represented in the form: