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Vicsek fractal (5th iteration of cross form) In mathematics the Vicsek fractal, also known as Vicsek snowflake or box fractal, [1] [2] is a fractal arising from a construction similar to that of the Sierpiński carpet, proposed by Tamás Vicsek. It has applications including as compact antennas, particularly in cellular phones.
Four iterations of a "box fractal" or "Vicsek fractal", derived by iteratively replacing a square with a saltire or cross of five smaller squares on a 3-by-3 subgrid. Top: Four iterations of the saltire form of the fractal. Bottom: Four iterations of the cross form of the fractal.
Fifth iteration of the cross (non-saltire) version of the "box fractal" or "Vicsek fractal", derived by iteratively replacing a square with a saltire or cross of five smaller squares on a 3-by-3 subgrid. For the first four iterations of both forms of the fractal, see Box or Vicsek Fractal 4-iterations.svg. Date: 2013: Source
The fifth iteration of the Vicsek fractal. If a sierpinski 4-gon were constructed from the given definition, the scale factor would be 1/2 and the fractal would simply be a square. A more interesting alternative, the Vicsek fractal, rarely called a quadraflake, is formed by successive flakes of five squares scaled by 1/3. Each flake is formed ...
The fractal is made up of the union of several copies of itself, each copy being transformed by a function (hence "function system"). The canonical example is the Sierpiński triangle . The functions are normally contractive , which means they bring points closer together and make shapes smaller.
When the length of the jump towards a vertex or another point is not 1/2, the chaos game generates other fractals, some of them very well-known. For example, when the jump is 2/3 and the point can also jump towards the center of the square, the chaos game generates the Vicsek fractal: A Vicsek fractal generated by the chaos game
Rauzy fractal; Rössler attractor; Sierpiński arrowhead curve; Sierpinski carpet; Sierpiński curve; Sierpinski triangle; Smith–Volterra–Cantor set; T-square; Takagi or Blancmange curve; Triflake [citation needed] Vicsek fractal; von Koch curve; Weierstrass function; Z-order curve
The Vicsek model is a mathematical model used to describe active ... indeed the phase diagram of the system exhibits a first order phase transition with a microphase ...