Sierpiński carpet
E735955
The Sierpiński carpet is a classic two-dimensional fractal formed by repeatedly removing central squares from a larger square, resulting in a highly intricate, self-similar pattern with zero area but infinite perimeter.
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
fractal
ⓘ
mathematical object ⓘ plane fractal ⓘ topological space ⓘ |
| area | 0 ⓘ |
| constructedFrom | unit square ⓘ |
| constructionStep |
divide square into 3x3 grid
ⓘ
remove open middle square ⓘ repeat process on each remaining subsquare ⓘ |
| definedAs | intersection of decreasing sequence of unions of closed squares ⓘ |
| dimension | 2 ⓘ |
| firstDescribedBy | Wacław Sierpiński NERFINISHED ⓘ |
| firstDescribedInYear | 1916 ⓘ |
| generalizationOf |
Cantor set
NERFINISHED
ⓘ
middle-third Cantor set to two dimensions ⓘ |
| hasAlternativeName | Sierpinski carpet NERFINISHED ⓘ |
| hasProperty |
fractal boundary
ⓘ
locally connected ⓘ nowhere dense in the square ⓘ nowhere differentiable boundary ⓘ perfect set ⓘ self-similar ⓘ totally disconnected interior ⓘ universal planar curve ⓘ |
| hasSymmetry |
fourfold rotational symmetry
ⓘ
reflection symmetry across horizontal axis ⓘ reflection symmetry across vertical axis ⓘ |
| HausdorffDimension | log(8)/log(3) ⓘ |
| HausdorffDimensionApprox | 1.8927892607 ⓘ |
| isBounded | true ⓘ |
| isClosed | true ⓘ |
| isCompact | true ⓘ |
| isConnected | true ⓘ |
| isLimitOf | sequence of compact sets ⓘ |
| isNowhereDense | true ⓘ |
| measure | Lebesgue measure zero ⓘ |
| namedAfter | Wacław Sierpiński NERFINISHED ⓘ |
| perimeter | infinite ⓘ |
| relatedTo |
Menger sponge
NERFINISHED
ⓘ
Sierpiński triangle NERFINISHED ⓘ |
| selfSimilarity | each of 8 subsquares is scaled copy of whole set ⓘ |
| subsetOf |
Euclidean plane
NERFINISHED
ⓘ
unit square [0,1]×[0,1] ⓘ |
| topologicalDimension | 1 ⓘ |
| usedIn |
complex dynamics
ⓘ
dynamical systems theory ⓘ fractal geometry ⓘ topology ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.