Lyapunov fractal
E181624
The Lyapunov fractal is a complex, self-similar pattern arising from iterating logistic maps with periodically varying parameters, used to visualize stability and chaos in dynamical systems.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Lyapunov fractal canonical | 3 |
| logistic map | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1597811 — 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: Lyapunov fractal Context triple: [Aleksandr Lyapunov, notableWork, Lyapunov fractal]
-
A.
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.
-
B.
Poincaré map
The Poincaré map is a mathematical tool in dynamical systems theory that reduces continuous-time dynamics to a discrete map by tracking intersections of trajectories with a lower-dimensional surface.
-
C.
Weierstrass function
The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
-
D.
Farey tessellation
The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
-
E.
NKS
NKS is the ICAO airline designator used in aviation to identify Spirit Airlines in flight operations and air traffic control.
- 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: Lyapunov fractal Target entity description: The Lyapunov fractal is a complex, self-similar pattern arising from iterating logistic maps with periodically varying parameters, used to visualize stability and chaos in dynamical systems.
-
A.
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.
-
B.
Poincaré map
The Poincaré map is a mathematical tool in dynamical systems theory that reduces continuous-time dynamics to a discrete map by tracking intersections of trajectories with a lower-dimensional surface.
-
C.
Weierstrass function
The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
-
D.
Farey tessellation
The Farey tessellation is a geometric partition of the hyperbolic plane into ideal triangles whose vertices correspond to rational numbers, closely linked to number theory and modular group actions.
-
E.
NKS
NKS is the ICAO airline designator used in aviation to identify Spirit Airlines in flight operations and air traffic control.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
fractal
ⓘ
mathematical object ⓘ visualization technique ⓘ |
| appliesTo |
logistic family of maps
ⓘ
one-dimensional maps ⓘ |
| basedOn |
Lyapunov exponent
ⓘ
linked to:
Lyapunov exponents
logistic map ⓘ |
| belongsTo |
field of complex systems
ⓘ
field of computational mathematics ⓘ field of scientific visualization ⓘ |
| computedBy |
evaluating Lyapunov exponent for each parameter sequence
ⓘ
iterating logistic map for each parameter pair ⓘ |
| dependsOn |
length of transient discarded
ⓘ
number of iterations ⓘ precision of numerical computation ⓘ |
| hasDomain |
chaos theory
ⓘ
dynamical systems ⓘ nonlinear dynamics ⓘ |
| hasProperty |
arises from iteration
ⓘ
complex structure ⓘ displays fractal boundaries ⓘ exhibits chaotic behavior ⓘ parameter-dependent ⓘ self-similar ⓘ |
| hasVisualizationType |
2D color plot
ⓘ
parameter-plane diagram ⓘ |
| namedAfter | Aleksandr Lyapunov ⓘ |
| outputEncoding |
color-coded Lyapunov exponent
ⓘ
color-coded stability vs chaos ⓘ |
| parameterSpace |
plane of two logistic parameters
ⓘ
space of periodic parameter sequences ⓘ |
| relatedTo |
Julia set
ⓘ
Lyapunov dimension ⓘ Lyapunov spectrum ⓘ
linked to:
Lyapunov exponents
Mandelbrot set ⓘ bifurcation diagram ⓘ |
| requires |
choice of initial condition
ⓘ
choice of parameter sequence pattern ⓘ |
| usedFor |
exploring parameter sensitivity
ⓘ
generating mathematical art ⓘ illustrating chaotic dynamics ⓘ studying bifurcations ⓘ |
| uses |
iterated maps
ⓘ
periodically varying parameters ⓘ |
| visualizes |
chaotic regions
ⓘ
sensitivity to initial conditions ⓘ stability regions ⓘ |
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: Lyapunov fractal Description of subject: The Lyapunov fractal is a complex, self-similar pattern arising from iterating logistic maps with periodically varying parameters, used to visualize stability and chaos in dynamical systems.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Lyapunov fractal