page_title: Vicsek fractal
hierarchical_section_title: Vicsek fractal
caption_attribution_description: English: A self-affine fractal set. Build iteratively from a p &#x00D7; q {\displaystyle \scriptstyle {p\times q}} array with p &#x2264; q {\displaystyle \scriptstyle {p\leq q}} . Its Hausdorff dimension equals log &#x2061; ( &#x2211; k = 1 p n k a ) / log &#x2061; p {\displaystyle \log {\left(\sum _{k=1}^{p}n_{k}^{a}\right)}/\log {p}} with a = log &#x2061; p / l o g q {\displaystyle a=\log {p}/log{q}} and n k {\displaystyle n_{k}} is the number of elements in the k t h {\displaystyle k^{th}} column. Here it is 1.8272. The box-countig dimension yields a different formula, therefore, a different value. Unlike self-similar sets, the Hausdorff dimension of self-affine sets depends on the position of the iterated elements and there is no formula, so far, for the general case
context_page_description: In mathematics the Vicsek fractal, also known as Vicsek snowflake or box fractal, is a fractal arising from a construction similar to that of the Sierpinski carpet, proposed by Tamás Vicsek. It has applications including as compact antennas, particularly in cellular phones.
  Box fractal also refers to various iterated fractals created by a square or rectangular grid with various boxes removed or absent and, at each iteration, those present and/or those absent have the previous image scaled down and drawn within them. The Sierpinski triangle may be approximated by a 2 × 2 box fractal with one corner removed. The Sierpinski carpet is a 3 × 3 box fractal with the middle square removed.
context_section_description: In mathematics the Vicsek fractal, also known as Vicsek snowflake or box fractal, is a fractal arising from a construction similar to that of the Sierpinski carpet, proposed by Tamás Vicsek. It has applications including as compact antennas, particularly in cellular phones.
  Box fractal also refers to various iterated fractals created by a square or rectangular grid with various boxes removed or absent and, at each iteration, those present and/or those absent have the previous image scaled down and drawn within them. The Sierpinski triangle may be approximated by a 2 × 2 box fractal with one corner removed. The Sierpinski carpet is a 3 × 3 box fractal with the middle square removed.
caption: Self-affine fractal built from a 3 × 2 grid
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