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In mathematics, a chaotic map is a map (namely, an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems.

Chaotic maps often generate fractals. Although a fractal may be constructed by an iterative procedure, some fractals are studied in and of themselves, as sets rather than in terms of the map that generates them. This is often because there are several different iterative procedures to generate the same fractal.

List of chaotic maps

List of fractals

• Cantor set
• de Rham curve
• Gravity set, or Mitchell-Green gravity set
• Julia set - derived from complex quadratic map
• Koch snowflake - special case of de Rham curve
• Lyapunov fractal
• Mandelbrot set - derived from complex quadratic map
• Menger sponge
• Newton fractal
• Nova fractal - derived from Newton fractal
• Quaternionic fractal - three dimensional complex quadratic map
• Sierpinski carpet
• Sierpinski triangle

References

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2. On the dynamics of a new simple 2-D rational discrete mapping
3. http://www.yangsky.us/ijcc/pdf/ijcc83/IJCC823.pdf
4. The Aizawa attractor
5. Local Stability and Hopf Bifurcation Analysis of the Arneodo’s System
6. Basin of attraction Archived 2014-07-01 at the Wayback Machine
7. Image encryption based on new Beta chaotic maps
8. 1981 The Burke & Shaw system
9. A new chaotic attractor coined
10. A new chaotic attractor coined
11. A new chaotic attractor coined
12. http://www.scholarpedia.org/article/Chua_circuit Chua Circuit
13. Clifford Attractors
14. Peter de Jong Attractors
15. A discrete population model of delayed regulation
16. Chaos from Euler Solution of ODEs
17. Chaos from Euler Solution of ODEs
18. Irregular Attractors
19. A New Finance Chaotic Attractor
20. Hyperchaos Archived 2015-12-22 at the Wayback Machine
21. Visions of Chaos 2D Strange Attractor Tutorial
22. A new chaotic system and beyond: The generalized Lorenz-like system
23. Gingerbreadman map
24. Mira Fractals
25. Half-inverted tearing
26. Halvorsen: A tribute to Dr. Edward Norton Lorenz
27. Peter de Jong Attractors
28. Hopalong orbit fractal
29. Irregular Attractors
30. Global chaos synchronization of hyperchaotic chen system by sliding model control
31. Hyper-Lu system
32. The first hyperchaotic system
33. Hyperchaotic attractor Archived 2015-12-22 at the Wayback Machine
34. Attractors
35. Knot fractal map Archived 2015-12-22 at the Wayback Machine
36. http://www.scholarpedia.org/article/Chaos_topology
37. A new discrete chaotic map based on the composition of permutations
38. A 3D symmetrical toroidal chaos
39. Lozi maps
40. Moore-Spiegel Attractor
41. A new chaotic system and beyond: The generalized lorenz-like system
42. A New Chaotic Jerk Circuit
43. Chaos Control and Hybrid Projective Synchronization of a Novel Chaotic System
44. Pickover
45. Polynomial Type-A
46. Polynomial Type-B
47. Polynomial Type-C
48. Quadrup Two Orbit Fractal
49. Rikitake chaotic attractor Archived 2010-06-20 at the Wayback Machine
50. Description of strange attractors using invariants of phase-plane
51. Skarya Archived 2015-12-22 at the Wayback Machine
52. Van der Pol Oscillator Equations
53. Shaw-Pol chaotic oscillator Archived 2015-12-22 at the Wayback Machine
54. The Shimiziu-Morioka System
55. Sprott B chaotic attractor Archived 2007-02-27 at the Wayback Machine
56. Chaos Blog - Sprott B system Archived 2015-12-22 at the Wayback Machine
57. Sprott C chaotic attractor Archived 2007-02-27 at the Wayback Machine
58. Chaos Blog - Sprott C system Archived 2015-12-22 at the Wayback Machine
59. Sprott's Gateway - Sprott-Linz A chaotic attractor Archived 2007-02-27 at the Wayback Machine
60. A new chaotic system and beyond: The generalized Lorenz-like System
61. Chaos Blog - Sprott-Linz A chaotic attractor Archived 2015-12-22 at the Wayback Machine
62. Sprott's Gateway - Sprott-Linz B chaotic attractor Archived 2007-02-27 at the Wayback Machine
63. A new chaotic system and beyond: The generalized Lorenz-like System
64. Chaos Blog - Sprott-Linz B chaotic attractor Archived 2015-12-22 at the Wayback Machine
65. Sprott's Gateway - Sprott-Linz C chaotic attractor Archived 2007-02-27 at the Wayback Machine
66. A new chaotic system and beyond: The generalized Lorenz-like System
67. Chaos Blog - Sprott-Linz C chaotic attractor Archived 2015-12-22 at the Wayback Machine
68. Sprott's Gateway - Sprott-Linz D chaotic attractor Archived 2007-02-27 at the Wayback Machine
69. A new chaotic system and beyond: The generalized Lorenz-like System
70. Chaos Blog - Sprott-Linz D chaotic attractor Archived 2015-12-22 at the Wayback Machine
71. Sprott's Gateway - Sprott-Linz E chaotic attractor Archived 2007-02-27 at the Wayback Machine
72. A new chaotic system and beyond: The generalized Lorenz-like System
73. Chaos Blog - Sprott-Linz E chaotic attractor Archived 2015-12-22 at the Wayback Machine
74. Sprott's Gateway - Sprott-Linz F chaotic attractor Archived 2007-02-27 at the Wayback Machine
75. A new chaotic system and beyond: The generalized Lorenz-like System
76. Chaos Blog - Sprott-Linz F chaotic attractor Archived 2015-12-22 at the Wayback Machine
77. Sprott's Gateway - Sprott-Linz G chaotic attractor Archived 2007-02-27 at the Wayback Machine
78. A new chaotic system and beyond: The generalized Lorenz-like System
79. Chaos Blog - Sprott-Linz G chaotic attractor Archived 2015-12-22 at the Wayback Machine
80. Sprott's Gateway - Sprott-Linz H chaotic attractor Archived 2007-02-27 at the Wayback Machine
81. A new chaotic system and beyond: The generalized Lorenz-like System
82. Chaos Blog - Sprott-Linz H chaotic attractor Archived 2015-12-22 at the Wayback Machine
83. Sprott's Gateway - Sprott-Linz I chaotic attractor Archived 2007-02-27 at the Wayback Machine
84. A new chaotic system and beyond: The generalized Lorenz-like System
85. Chaos Blog - Sprott-Linz I chaotic attractor Archived 2015-12-22 at the Wayback Machine
86. Sprott's Gateway - Sprott-Linz J chaotic attractor Archived 2007-02-27 at the Wayback Machine
87. A new chaotic system and beyond: The generalized Lorenz-like System
88. Chaos Blog - Sprott-Linz J chaotic attractor Archived 2015-12-22 at the Wayback Machine
89. Sprott's Gateway - Sprott-Linz K chaotic attractor Archived 2007-02-27 at the Wayback Machine
90. A new chaotic system and beyond: The generalized Lorenz-like System
91. Chaos Blog - Sprott-Linz K chaotic attractor Archived 2015-12-22 at the Wayback Machine
92. Sprott's Gateway - Sprott-Linz L chaotic attractor Archived 2007-02-27 at the Wayback Machine
93. A new chaotic system and beyond: The generalized Lorenz-like System
94. Chaos Blog - Sprott-Linz L chaotic attractor Archived 2015-12-22 at the Wayback Machine
95. Sprott's Gateway - Sprott-Linz M chaotic attractor Archived 2007-02-27 at the Wayback Machine
96. A new chaotic system and beyond: The generalized Lorenz-like System
97. Chaos Blog - Sprott-Linz M chaotic attractor Archived 2015-12-22 at the Wayback Machine
98. Sprott's Gateway - Sprott-Linz N chaotic attractor Archived 2007-02-27 at the Wayback Machine
99. A new chaotic system and beyond: The generalized Lorenz-like System
100. Chaos Blog - Sprott-Linz N chaotic attractor Archived 2015-12-22 at the Wayback Machine
101. Sprott's Gateway - Sprott-Linz O chaotic attractor Archived 2007-02-27 at the Wayback Machine
102. A new chaotic system and beyond: The generalized Lorenz-like System
103. Chaos Blog - Sprott-Linz O chaotic attractor Archived 2015-12-22 at the Wayback Machine
104. Sprott's Gateway - Sprott-Linz P chaotic attractor Archived 2007-02-27 at the Wayback Machine
105. A new chaotic system and beyond: The generalized Lorenz-like System
106. Chaos Blog - Sprott-Linz P chaotic attractor Archived 2015-12-22 at the Wayback Machine
107. Sprott's Gateway - Sprott-Linz Q chaotic attractor Archived 2007-02-27 at the Wayback Machine
108. A new chaotic system and beyond: The generalized Lorenz-like System
109. Chaos Blog - Sprott-Linz Q chaotic attractor Archived 2015-12-22 at the Wayback Machine
110. Sprott's Gateway - Sprott-Linz R chaotic attractor Archived 2007-02-27 at the Wayback Machine
111. A new chaotic system and beyond: The generalized Lorenz-like System
112. Chaos Blog - Sprott-Linz R chaotic attractor Archived 2015-12-22 at the Wayback Machine
113. Sprott's Gateway - Sprott-Linz S chaotic attractor Archived 2007-02-27 at the Wayback Machine
114. A new chaotic system and beyond: The generalized Lorenz-like System
115. Chaos Blog - Sprott-Linz S chaotic attractor Archived 2015-12-22 at the Wayback Machine
116. Strizhak-Kawczynski chaotic oscillator
117. Chaos Blog - Strizhak-Kawczynski chaotic oscillator Archived 2015-12-22 at the Wayback Machine
118. Sprott's Gateway - A symmetric chaotic flow
119. http://sprott.physics.wisc.edu/chaostsa/ Sprott's Gateway - Chaos and Time-Series Analysis
120. Oscillator of Ueda
121. Internal fluctuations in a model of chemical chaos
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123. Synchronization of Chaotic Fractional-Order WINDMI Systems via Linear State Error Feedback Control
124. Adaptive Backstepping Controller Design for the Anti-Synchronization of Identical WINDMI Chaotic Systems with Unknown Parameters and its SPICE Implementation
125. Chen, Guanrong; Kudryashova, Elena V.; Kuznetsov, Nikolay V.; Leonov, Gennady A. (2016). "Dynamics of the Zeraoulia–Sprott Map Revisited". International Journal of Bifurcation and Chaos. 26 (7): 1650126–21. arXiv:1602.08632. Bibcode:2016IJBC...2650126C. doi:10.1142/S0218127416501261. S2CID 11406449.

v t e Chaos theory
Concepts	Core Attractor Bifurcation Fractal Limit set Lyapunov exponent Orbit Periodic point Phase space Anosov diffeomorphism Arnold tongue axiom A dynamical system Bifurcation diagram Box-counting dimension Correlation dimension Conservative system Ergodicity False nearest neighbors Hausdorff dimension Invariant measure Lyapunov stability Measure-preserving dynamical system Mixing Poincaré section Recurrence plot SRB measure Stable manifold Topological conjugacy Theorems Ergodic theorem Liouville's theorem Krylov–Bogolyubov theorem Poincaré–Bendixson theorem Poincaré recurrence theorem Stable manifold theorem Takens's theorem
Theoretical branches	Bifurcation theory Control of chaos Dynamical system Ergodic theory Quantum chaos Stability theory Synchronization of chaos
Chaotic maps (list)	Discrete Arnold's cat map Baker's map Complex quadratic map Coupled map lattice Duffing map Dyadic transformation Dynamical billiards outer Exponential map Gauss map Gingerbreadman map Hénon map Horseshoe map Ikeda map Interval exchange map Irrational rotation Kaplan–Yorke map Langton's ant Logistic map Standard map Tent map Tinkerbell map Zaslavskii map Continuous Double scroll attractor Duffing equation Lorenz system Lotka–Volterra equations Mackey–Glass equations Rabinovich–Fabrikant equations Rössler attractor Three-body problem Van der Pol oscillator
Physical systems	Chua's circuit Convection Double pendulum Elastic pendulum FPUT problem Hénon–Heiles system Kicked rotator Multiscroll attractor Population dynamics Swinging Atwood's machine Tilt-A-Whirl Weather
Chaos theorists	Michael Berry Rufus Bowen Mary Cartwright Chen Guanrong Leon O. Chua Mitchell Feigenbaum Peter Grassberger Celso Grebogi Martin Gutzwiller Brosl Hasslacher Michel Hénon Svetlana Jitomirskaya Bryna Kra Edward Norton Lorenz Aleksandr Lyapunov Benoît Mandelbrot Hee Oh Edward Ott Henri Poincaré Itamar Procaccia Mary Rees Otto Rössler David Ruelle Caroline Series Yakov Sinai Oleksandr Mykolayovych Sharkovsky Nina Snaith Floris Takens Audrey Terras Mary Tsingou Marcelo Viana Amie Wilkinson James A. Yorke Lai-Sang Young
Related articles	Butterfly effect Complexity Edge of chaos Predictability Santa Fe Institute

• Chaotic maps
• Mathematics-related lists