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Gaps, carpets and branches

  1. 1

    Sierpiński triangle

    Recursive construction

  2. 2

    Sierpiński carpet

    Recursive construction

  3. 3

    Cantor set

    Recursive construction

  4. 4

    Vicsek fractal

    Recursive construction

  5. 5

    Pythagoras tree

    Recursive construction

  6. 6

    Barnsley fern

    Iterated function system

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About this collection6 items

Sierpiński triangle and carpet, Cantor set, Vicsek fractal, Pythagoras tree and Barnsley fern.

A themed selection by Fav Tings. Display order is for browsing, not a ranking.

Numbers show collection order, not a source rating.

  1. Sierpiński triangle — Recursive construction
  2. Sierpiński carpet — Recursive construction
  3. Cantor set — Recursive construction
  4. Vicsek fractal — Recursive construction
  5. Pythagoras tree — Recursive construction
  6. Barnsley fern — Iterated function system
Fractal sources
  1. Sierpiński triangle: definition reference · Hausdorff dimension log 3 / log 2 ≈ 1.585 (set) · Depth-5 approximation (243 cells), filled and fitted to a 448px square.
  2. Sierpiński carpet: definition reference · Hausdorff dimension log 8 / log 3 ≈ 1.8928 (set) · Depth-4 approximation (586 cells), filled and fitted to a 448px square.
  3. Cantor set: definition reference · Hausdorff dimension log 2 / log 3 ≈ 0.6309 (set) · Levels 0–5 stacked top to bottom (63 cells), filled and fitted to a 448px square.
  4. Vicsek fractal: definition reference · Hausdorff dimension log 5 / log 3 ≈ 1.465 (set) · Depth-4 approximation (625 cells), filled and fitted to a 448px square.
  5. Pythagoras tree: definition reference · Hausdorff dimension 2 ≈ 2 (set (45° tree)) · Depth-10 approximation with 45° branches (2,047 cells), filled and fitted to a 448px square.
  6. Barnsley fern: definition reference · Point-cloud approximation of the attractor by the chaos game: 1,500,000 points from fixed seed 19, a square window of side 11.4266 centered at (0.2369, 4.9992).

Fractal images are illustrations rendered by Fav Tings from each construction’s published definition; a finite image only approximates the infinite object. References are English Wikipedia articles, used as factual cross-references; nothing is copied from them.

Fractals: illustrations rendered by Fav Tings from published definitions · references: Wikipedia.