Fractal Perimeter Calculator
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Understanding Fractal Geometry
What are Fractals?
Fractals are geometric shapes that exhibit self-similarity at different scales, often having non-integer dimensions.
Fractal Dimension = log(N)/log(1/r)
Perimeter Length = L₀ × (r × N)ⁿ
where:
- N = number of segments per iteration
- r = scaling factor
- L₀ = initial length
- n = number of iterations
Types of Fractals
- Geometric Fractals:
- Koch Snowflake (D ≈ 1.2619)
- Sierpinski Triangle (D ≈ 1.5850)
- Dragon Curve (D ≈ 2.0000)
- Hilbert Curve (D = 2.0000)
- Natural Fractals:
- Coastlines
- Tree Branching
- Blood Vessels
- Mountain Ranges
- Properties:
- Self-Similarity
- Infinite Detail
- Non-Integer Dimension
- Recursive Definition
Advanced Concepts
Hausdorff Dimension
Measure of complexity
Box-Counting
Numerical dimension
Similarity Dimension
Self-similar scaling
Fractal Growth
Pattern formation