Enter the infinite realm where mathematics meets art. Each click, scroll, and zoom reveals new layers of complexity, following the golden ratio φ = 1.618... that governs natural beauty.
Navigate through self-similar patterns that repeat endlessly at every scale. Discover the infinite depth hidden within finite boundaries.
The most famous fractal, defined by the simple equation z² + c. Its boundary contains infinite complexity, with spiral arms and self-similar miniature copies appearing at every zoom level.
Zoom depth: 1 → ∞. Each iteration reveals new mathematical poetry written in the language of complex numbers.
For each point c in the complex plane, there exists a unique Julia set. Connected sets form intricate, filled shapes while disconnected sets create Cantor dust - infinite sparse structures.
Interactive parameter: c = φ + φi creates particularly elegant connected Julia sets.
The Sierpinski triangle demonstrates perfect self-similarity. Start with a triangle, remove the center triangle, repeat forever. The result has zero area but infinite perimeter.
Dimension: log(3)/log(2) ≈ 1.585 - between a line and a plane, existing in fractional dimensions.
Fold a strip of paper infinitely many times, then unfold it at right angles. The result is the dragon curve - a space-filling curve that never intersects itself.
Generation n+1 = Generation n + (90° turn) + (Generation n reversed). Infinite complexity from simple rules.
The Fibonacci sequence converges to φ, appearing in nautilus shells, galaxy arms, and flower petals. The golden spiral grows by a factor of φ every quarter turn.
φ = (1 + √5)/2 ≈ 1.618033988749... The most irrational number, resisting rational approximation.
Recursively creating new fractal dimensions...