T-square (fractal)
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{{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)]]