T-square (fractal) 1227275 203327868 2008-04-04T17:28:38Z Giftlite 37986 [[WP:UNDO|Undid]] revision 203316141 by [[Special:Contributions/64.75.117.146|64.75.117.146]] ([[User talk:64.75.117.146|talk]]) {{This|a two dimensional fractal in mathematics|T-square (disambiguation)}} In [[mathematics]], the '''T-square''' is a two-dimensional [[fractal]]. As all two-dimensional fractals, it has a boundary of infinite length bounding a finite area. Its name follows from that for a [[T-square]]. [[Image:T-Square fractal (evolution).png|T-square, evolution in six steps.]]<br clear=all> ==Algorithmic description== It can be generated from using this [[algorithm]]: # Image 1: ## Start with a square. ## Subtract a square half the original length and width (one-quarter the area) from the center. # Image 2: ## Start with the previous image. ## Scale down a copy to one-half the original length and width. ## From each of the quadrants of Image 1, subtract the copy of the image. # Images 3-6: ## Repeat step 2. [[Image:T-Square fractal (8 iterations).png|thumb|256px|'''T-square'''.]] The method of creation is rather similar to the ones used to create a [[Koch snowflake]] or a [[Sierpinski triangle]]. ==Properties== T-square has a [[fractal dimension]] of ln(4)/ln(2) = 2. The black surface extent is ''almost'' everywhere in the bigger square, for, once a point has been darkened, it remains black for every other iteration ; however some points remain white. The limit curve is a fractal line, of fractal dimension 2. ==See also== *[[List of fractals by Hausdorff dimension]] *[[Sierpinski carpet]] [[Category:Fractals]] [[bs:T-linijar (fraktal)]] [[hr:T-ravnalo (fraktal)]]