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.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Sierpiński carpet canonical | 2 |
| Sierpinski carpet | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T8454681 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Sierpiński carpet Context triple: [Menger sponge, relatedTo, Sierpiński carpet]
-
A.
Menger sponge
The Menger sponge is a classic three-dimensional fractal object characterized by infinite surface area and zero volume, constructed by recursively removing cubes from a larger cube.
-
B.
Peano curve
The Peano curve is a space-filling fractal curve that continuously maps a one-dimensional interval onto a two-dimensional area, demonstrating that a line can completely fill a square.
-
C.
Mandelbrot set
The Mandelbrot set is a famous complex-plane fractal defined by iterating quadratic polynomials, known for its infinitely intricate boundary and iconic role in chaos theory and complex dynamics.
-
D.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
E.
Julia set
A Julia set is a complex fractal formed by iterating a function on the complex plane, often producing intricate, self-similar boundary patterns that are central objects in complex dynamics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Sierpiński carpet Target entity description: 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.
-
A.
Menger sponge
The Menger sponge is a classic three-dimensional fractal object characterized by infinite surface area and zero volume, constructed by recursively removing cubes from a larger cube.
-
B.
Peano curve
The Peano curve is a space-filling fractal curve that continuously maps a one-dimensional interval onto a two-dimensional area, demonstrating that a line can completely fill a square.
-
C.
Mandelbrot set
The Mandelbrot set is a famous complex-plane fractal defined by iterating quadratic polynomials, known for its infinitely intricate boundary and iconic role in chaos theory and complex dynamics.
-
D.
Ulam spiral
The Ulam spiral is a graphical arrangement of the positive integers in a spiral pattern that reveals striking diagonal alignments of prime numbers, suggesting unexpected structure in their distribution.
-
E.
Julia set
A Julia set is a complex fractal formed by iterating a function on the complex plane, often producing intricate, self-similar boundary patterns that are central objects in complex dynamics.
- F. None of above. chosen
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 ⓘ |
| firstDescribedInYear | 1916 ⓘ |
| generalizationOf |
Cantor set
ⓘ
middle-third Cantor set to two dimensions ⓘ |
| hasAlternativeName |
Sierpinski carpet
ⓘ
linked to:
Sierpiński carpet
|
| 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 ⓘ |
| perimeter | infinite ⓘ |
| relatedTo |
Menger sponge
ⓘ
Sierpiński triangle ⓘ
linked to:
Sierpiński gasket
|
| selfSimilarity | each of 8 subsquares is scaled copy of whole set ⓘ |
| subsetOf |
Euclidean plane
ⓘ
unit square [0,1]×[0,1] ⓘ |
| topologicalDimension | 1 ⓘ |
| usedIn |
complex dynamics
ⓘ
dynamical systems theory ⓘ fractal geometry ⓘ topology ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Sierpiński carpet Description of subject: 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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Sierpiński carpet