Fractals: Peano curve
Repeat one simple rule and watch the detail build. Choose a classic fractal and its depth, then download it in your colors or as black lines.
The first space-filling curve: one unbroken line that zigzags through every cell of a grid three times as wide at each depth.
Drawing fractal…
Sources
- Benoit B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, 1982. The book that named and popularized fractals, background for the fractal maker.
- Helge von Koch, Sur une courbe continue sans tangente, obtenue par une construction géométrique élémentaire, Arkiv för Matematik 1, 1904. The Koch snowflake in the fractal maker is named for this paper.
- Wacław Sierpiński, Sur une courbe dont tout point est un point de ramification, Comptes Rendus de l'Académie des Sciences 160, 1915. The Sierpiński triangle in the fractal maker is named for this paper.
- David Hilbert, Über die stetige Abbildung einer Linie auf ein Flächenstück, Mathematische Annalen 38, 1891. The Hilbert curve in the fractal maker is named for this paper.
- Paul Lévy, Les courbes planes ou gauches et les surfaces composées de parties semblables au tout, Journal de l'École Polytechnique, 1938. The Lévy C curve in the fractal maker is named for this paper.
- Giuseppe Peano, Sur une courbe, qui remplit toute une aire plane, Mathematische Annalen 36, 1890. The Peano curve in the fractal maker is named for this paper.
- Przemysław Prusinkiewicz and Aristid Lindenmayer, The Algorithmic Beauty of Plants, Springer-Verlag, 1990. The rules for the L-system plant in the fractal maker come from figure 1.24f of this book.