List of chaotic maps

Short description: none

In mathematics, a chaotic map is a map (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 and iterated functions often generate fractals. Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal. See also Universality (dynamical systems).

## List of chaotic maps

Map | Time domain | Space domain | Number of space dimensions | Number of parameters | Also known as

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2D Lorenz system[1] | discrete | real | 2 | 1 | Euler method approximation to (non-chaotic) ODE.
2D Rational chaotic map[2] | discrete | rational | 2 | 2 |
3-cells CNN system | continuous | real | 3 |  |
ACT chaotic attractor[3] | continuous | real | 3 |  |
Aizawa chaotic attractor[4] | continuous | real | 3 | 5 |
Arneodo chaotic system[5] | continuous | real | 3 |  |
Arnold's cat map | discrete | real | 2 | 0 |
Baker's map | discrete | real | 2 | 0 |
Basin chaotic map[6] | discrete | real | 2 | 1 |
Beta Chaotic Map[7] |  |  |  | 12 |
Bogdanov map | discrete | real | 2 | 3 |
Brusselator | continuous | real | 3 |  |
Burke-Shaw chaotic attractor[8] | continuous | real | 3 | 2 |
Chen chaotic attractor[9] | continuous | real | 3 | 3 | Not topologically conjugate to the Lorenz attractor.
Chen-Celikovsky system[10] | continuous | real | 3 |  | "Generalized Lorenz canonical form of chaotic systems"
Chen-LU system[11] | continuous | real | 3 | 3 | Interpolates between Lorenz-like and Chen-like behavior.
Chen-Lee system | continuous | real | 3 |  |
Chialvo map  | discrete  | discrete  |  | 3  |
Chossat-Golubitsky symmetry map |  |  |  |  |
Chua circuit[12] | continuous | real | 3 | 3 |
Circle map | discrete | real | 1 | 2 |
Complex quadratic map | discrete | complex | 1 | 1 | gives rise to the Mandelbrot set
Complex squaring map | discrete | complex | 1 | 0 | acts on the Julia set for the squaring map.
Complex cubic map | discrete | complex | 1 | 2 |
Clifford fractal map[13] | discrete | real | 2 | 4 |
Degenerate Double Rotor map |  |  |  |  |
De Jong fractal map[14] | discrete | real | 2 | 4 |
Delayed-Logistic system[15] | discrete | real | 2 | 1 |
Discretized circular Van der Pol system[16] | discrete | real | 2 | 1 | Euler method approximation to 'circular' Van der Pol-like ODE.
Discretized Van der Pol system[17] | discrete | real | 2 | 2 | Euler method approximation to Van der Pol ODE.
Double rotor map |  |  |  |  |
Duffing map | discrete | real | 2 | 2 | Holmes chaotic map
Duffing equation | continuous | real | 2 | 5 (3 independent) |
Dyadic transformation | discrete | real | 1 | 0 | 2x mod 1 map, Bernoulli map, doubling map, sawtooth map
Exponential map | discrete | complex | 2 | 1 |
Feigenbaum strange nonchaotic map[18] | discrete | real | 3 |  |
Finance system[19] | continuous | real | 3 |  |
Folded-Towel hyperchaotic map[20] | continuous | real | 3 |  |
Fractal-Dream system[21] | discrete | real | 2 |  |
Gauss map | discrete | real | 1 |  | mouse map, Gaussian map
Generalized Baker map |  |  |  |  |
Genesio-Tesi chaotic attractor[22] | continuous | real | 3 |  |
Gingerbreadman map[23] | discrete | real | 2 | 0 |
Grinch dragon fractal | discrete | real | 2 |  |
Gumowski/Mira map[24] | discrete | real | 2 | 1 |
Hadley chaotic circulation | continuous | real | 3 | 0 |
Half-inverted Rössler attractor[25] |  |  |  |  |
Halvorsen chaotic attractor[26] | continuous | real | 3 |  |
Hénon map | discrete | real | 2 | 2 |
Hénon with 5th order polynomial |  |  |  |  |
Hindmarsh-Rose neuronal model | continuous | real | 3 | 8 |
Hitzl-Zele map |  |  |  |  |
Horseshoe map | discrete | real | 2 | 1 |
Hopa-Jong fractal[27] | discrete | real | 2 |  |
Hopalong orbit fractal[28] | discrete | real | 2 |  |
Hyper Logistic map[29] | discrete | real | 2 |  |
Hyperchaotic Chen system[30] | continuous | real | 3 |  |
Hyper Newton-Leipnik system | continuous | real | 4 |  |
Hyper-Lorenz chaotic attractor | continuous | real | 4 |  |
Hyper-Lu chaotic system[31] | continuous | real | 4 |  |
Hyper-Rössler chaotic attractor[32] | continuous | real | 4 |  |
Hyperchaotic attractor[33] | continuous | real | 4 |  |
Ikeda chaotic attractor[34] | continuous | real | 3 |  |
Ikeda map | discrete | real | 2 | 3 | Ikeda fractal map
Interval exchange map | discrete | real | 1 | variable |
Kaplan-Yorke map | discrete | real | 2 | 1 |
Knot fractal map[35] | discrete | real | 2 |  |
Knot-Holder chaotic oscillator[36] | continuous | real | 3 |  |
Kuramoto–Sivashinsky equation | continuous | real |  |  |
Lambić map[37] | discrete | discrete | 1 |  |
Li symmetrical toroidal chaos[38] | continuous | real | 3 |  |
Linear map on unit square |  |  |  |  |
Logistic map | discrete | real | 1 | 1 |
Lorenz system | continuous | real | 3 | 3 |
Lorenz system's Poincaré return map | discrete | real | 2 | 3 |
Lorenz 96 model | continuous | real | arbitrary | 1 |
Lotka-Volterra system | continuous | real | 3 | 9 |
Lozi map[39] | discrete | real | 2 |  |
Moore-Spiegel chaotic oscillator[40] | continuous | real | 3 |  |
Scroll-Attractor[41] | continuous | real | 3 |  |
Jerk Circuit[42] | continuous | real | 3 |  |
Newton-Leipnik system | continuous | real | 3 |  |
Nordmark truncated map |  |  |  |  |
Nosé-Hoover system | continuous | real | 3 |  |
Novel chaotic system[43] | continuous | real | 3 |  |
Pickover fractal map[44] | continuous | real | 3 |  |
Pomeau-Manneville maps for intermittent chaos | discrete | real | 1 or 2 |  | Normal-form maps for intermittency (Types I, II and III)
Polynom Type-A fractal map[45] | continuous | real | 3 | 3 |
Polynom Type-B fractal map[46] | continuous | real | 3 | 6 |
Polynom Type-C fractal map[47] | continuous | real | 3 | 18 |
Pulsed rotor |  |  |  |  |
Quadrup-Two orbit fractal[48] | discrete | real | 2 | 3 |
Quasiperiodicity map |  |  |  |  |
Mikhail Anatoly chaotic attractor | continuous | real | 3 | 2 |
Random Rotate map |  |  |  |  |
Rayleigh-Benard chaotic oscillator | continuous | real | 3 | 3 |
Rikitake chaotic attractor[49] | continuous | real | 3 | 3 |
Rössler attractor | continuous | real | 3 | 3 |
Rucklidge system[50] | continuous | real | 3 | 2 |
Sakarya chaotic attractor[51] | continuous | real | 3 | 2 |
Shaw-Pol chaotic oscillator[52][53] | continuous | real | 3 | 3 |
Shimizu-Morioka system[54] | continuous | real | 3 | 2 |
Shobu-Ose-Mori piecewise-linear map | discrete | real | 1 |  | piecewise-linear approximation for Pomeau-Manneville Type I map
Sinai map - [2][3] |  |  |  |  |
Sprott B chaotic system[55][56] | continuous | real | 3 | 2 |
Sprott C chaotic system[57][58] | continuous | real | 3 | 3 |
Sprott-Linz A chaotic attractor[59][60][61] | continuous | real | 3 | 0 |
Sprott-Linz B chaotic attractor[62][63][64] | continuous | real | 3 | 0 |
Sprott-Linz C chaotic attractor[65][66][67] | continuous | real | 3 | 0 |
Sprott-Linz D chaotic attractor[68][69][70] | continuous | real | 3 | 1 |
Sprott-Linz E chaotic attractor[71][72][73] | continuous | real | 3 | 1 |
Sprott-Linz F chaotic attractor[74][75][76] | continuous | real | 3 | 1 |
Sprott-Linz G chaotic attractor[77][78][79] | continuous | real | 3 | 1 |
Sprott-Linz H chaotic attractor[80][81][82] | continuous | real | 3 | 1 |
Sprott-Linz I chaotic attractor[83][84][85] | continuous | real | 3 | 1 |
Sprott-Linz J chaotic attractor[86][87][88] | continuous | real | 3 | 1 |
Sprott-Linz K chaotic attractor[89][90][91] | continuous | real | 3 | 1 |
Sprott-Linz L chaotic attractor[92][93][94] | continuous | real | 3 | 2 |
Sprott-Linz M chaotic attractor[95][96][97] | continuous | real | 3 | 1 |
Sprott-Linz N chaotic attractor[98][99][100] | continuous | real | 3 | 1 |
Sprott-Linz O chaotic attractor[101][102][103] | continuous | real | 3 | 1 |
Sprott-Linz P chaotic attractor[104][105][106] | continuous | real | 3 | 1 |
Sprott-Linz Q chaotic attractor[107][108][109] | continuous | real | 3 | 2 |
Sprott-Linz R chaotic attractor[110][111][112] | continuous | real | 3 | 2 |
Sprott-Linz S chaotic attractor[113][114][115] | continuous | real | 3 | 1 |
Standard map, Kicked rotor | discrete | real | 2 | 1 | Chirikov standard map, Chirikov-Taylor map
Strizhak-Kawczynski chaotic oscillator[116][117] | continuous | real | 3 | 9 |
Symmetric Flow attractor[118] | continuous | real | 3 | 1 |
Symplectic map |  |  |  |  |
Tangent map |  |  |  |  |
Tahn map[119] | discrete | real | 1 | 1 | Ring laser map [120]Beta distribution[121]

[122]

Thomas' cyclically symmetric attractor[123] | continuous | real | 3 | 1 |
Tent map | discrete | real | 1 |  |
Tinkerbell map | discrete | real | 2 | 4 |
Triangle map |  |  |  |  |
Ueda chaotic oscillator[124] | continuous | real | 3 | 3 |
Van der Pol oscillator | continuous | real | 2 | 3 |
Weierstrass map[125] | discrete  | real  | 1  | 4  | Gives rise to arbitrarily large global Lyapunov exponent
Willamowski-Rössler model[126] | continuous | real | 3 | 10 |
WINDMI chaotic attractor[127][128][129] | continuous | real | 1 | 2 |
Zaslavskii map | discrete | real | 2 | 4 |
Zaslavskii rotation map |  |  |  |  |
Zeraoulia-Sprott map[130] | discrete | real | 2 | 2 |

## List of fractals

See also: List of fractals by Hausdorff dimension

* 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

1. ↑ Chaos from Euler Solution of ODEs
2. ↑ On the dynamics of a new simple 2-D rational discrete mapping
3. ↑ [1][Usurped!]
4. ↑ The Aizawa attractor
5. ↑ Local Stability and Hopf Bifurcation Analysis of the Arneodo's System
6. ↑ Basin of attraction
7. ↑ Zahmoul, Rim; Ejbali, Ridha; Zaied, Mourad (2017). "Image encryption based on new Beta chaotic maps" (in en). Optics and Lasers in Engineering 96: 39–49. doi:10.1016/j.optlaseng.2017.04.009. Bibcode: 2017OptLE..96...39Z. https://linkinghub.elsevier.com/retrieve/pii/S0143816617300775.
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
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[Usurped!]
31. ↑ Hyper-Lu system
32. ↑ The first hyperchaotic system
33. ↑ Hyperchaotic attractor
34. ↑ Attractors
35. ↑ Knot fractal map
36. ↑ Lefranc, Marc; Letellier, Christophe; Gilmore, Robert (2008). "Chaos topology". Scholarpedia 3 (7): 4592. doi:10.4249/scholarpedia.4592. Bibcode: 2008SchpJ...3.4592G.
37. ↑ Lambić, Dragan (2015). "A new discrete chaotic map based on the composition of permutations" (in en). Chaos, Solitons & Fractals 78: 245–248. doi:10.1016/j.chaos.2015.08.001. Bibcode: 2015CSF....78..245L. https://linkinghub.elsevier.com/retrieve/pii/S0960077915002325.
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
50. ↑ Description of strange attractors using invariants of phase-plane
51. ↑ Skarya
52. ↑ Van der Pol Oscillator Equations
53. ↑ Shaw-Pol chaotic oscillator
54. ↑ The Shimiziu-Morioka System
55. ↑ Sprott B chaotic attractor
56. ↑ Chaos Blog - Sprott B system
57. ↑ Sprott C chaotic attractor
58. ↑ Chaos Blog - Sprott C system
59. ↑ Sprott's Gateway - Sprott-Linz A chaotic attractor
60. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
61. ↑ Chaos Blog - Sprott-Linz A chaotic attractor
62. ↑ Sprott's Gateway - Sprott-Linz B chaotic attractor
63. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
64. ↑ Chaos Blog - Sprott-Linz B chaotic attractor
65. ↑ Sprott's Gateway - Sprott-Linz C chaotic attractor
66. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
67. ↑ Chaos Blog - Sprott-Linz C chaotic attractor
68. ↑ Sprott's Gateway - Sprott-Linz D chaotic attractor
69. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
70. ↑ Chaos Blog - Sprott-Linz D chaotic attractor
71. ↑ Sprott's Gateway - Sprott-Linz E chaotic attractor
72. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
73. ↑ Chaos Blog - Sprott-Linz E chaotic attractor
74. ↑ Sprott's Gateway - Sprott-Linz F chaotic attractor
75. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
76. ↑ Chaos Blog - Sprott-Linz F chaotic attractor
77. ↑ Sprott's Gateway - Sprott-Linz G chaotic attractor
78. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
79. ↑ Chaos Blog - Sprott-Linz G chaotic attractor
80. ↑ Sprott's Gateway - Sprott-Linz H chaotic attractor
81. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
82. ↑ Chaos Blog - Sprott-Linz H chaotic attractor
83. ↑ Sprott's Gateway - Sprott-Linz I chaotic attractor
84. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
85. ↑ Chaos Blog - Sprott-Linz I chaotic attractor
86. ↑ Sprott's Gateway - Sprott-Linz J chaotic attractor
87. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
88. ↑ Chaos Blog - Sprott-Linz J chaotic attractor
89. ↑ Sprott's Gateway - Sprott-Linz K chaotic attractor
90. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
91. ↑ Chaos Blog - Sprott-Linz K chaotic attractor
92. ↑ Sprott's Gateway - Sprott-Linz L chaotic attractor
93. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
94. ↑ Chaos Blog - Sprott-Linz L chaotic attractor
95. ↑ Sprott's Gateway - Sprott-Linz M chaotic attractor
96. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
97. ↑ Chaos Blog - Sprott-Linz M chaotic attractor
98. ↑ Sprott's Gateway - Sprott-Linz N chaotic attractor
99. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
100. ↑ Chaos Blog - Sprott-Linz N chaotic attractor
101. ↑ Sprott's Gateway - Sprott-Linz O chaotic attractor
102. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
103. ↑ Chaos Blog - Sprott-Linz O chaotic attractor
104. ↑ Sprott's Gateway - Sprott-Linz P chaotic attractor
105. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
106. ↑ Chaos Blog - Sprott-Linz P chaotic attractor
107. ↑ Sprott's Gateway - Sprott-Linz Q chaotic attractor
108. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
109. ↑ Chaos Blog - Sprott-Linz Q chaotic attractor
110. ↑ Sprott's Gateway - Sprott-Linz R chaotic attractor
111. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
112. ↑ Chaos Blog - Sprott-Linz R chaotic attractor
113. ↑ Sprott's Gateway - Sprott-Linz S chaotic attractor
114. ↑ A new chaotic system and beyond: The generalized Lorenz-like System
115. ↑ Chaos Blog - Sprott-Linz S chaotic attractor
116. ↑ Strizhak-Kawczynski chaotic oscillator
117. ↑ Chaos Blog - Strizhak-Kawczynski chaotic oscillator
118. ↑ Sprott's Gateway - A symmetric chaotic flow
119. ↑ Okulov, A. Yu (2020). "Structured light entities, chaos and nonlocal maps". Chaos, Solitons & Fractals 133. doi:10.1016/j.chaos.2020.109638. Bibcode: 2020CSF...13309638O. http://doi:10.1016/j.chaos.2020.109638.
120. ↑ Okulov, A. Yu.; Oraevsky, A. N. (1986). "Space–temporal behavior of a light pulse propagating in a nonlinear nondispersive medium". Journal of the Optical Society of America B 3 (5): 741. doi:10.1364/JOSAB.3.000741. Bibcode: 1986JOSAB...3..741O.
121. ↑ Okulov, A Yu; Oraevskiĭ, A. N. (1984). "Regular and stochastic self-modulation of radiation in a ring laser with a nonlinear element". Soviet Journal of Quantum Electronics 14 (9): 1235–1237. doi:10.1070/QE1984v014n09ABEH006171. https://iopscience.iop.org/article/10.1070/QE1984v014n09ABEH006171.
122. ↑ Okulov, Alexey Yurievich (2020). "Numerical investigation of coherent and turbulent structures of light via nonlinear integral mappings". Computer Research and Modeling 12 (5): 979–992. doi:10.20537/2076-7633-2020-12-5-979-992. http://doi:10.20537/2076-7633-2020-12-5-979-992.
123. ↑ http://sprott.physics.wisc.edu/chaostsa/ Sprott's Gateway - Chaos and Time-Series Analysis
124. ↑ Oscillator of Ueda
125. ↑ McCartney, Mark. "A monster map: chaos on a prefractal". International Journal of Mathematical Education in Science and Technology. https://www.tandfonline.com/doi/full/10.1080/0020739X.2025.2539713#d1e101.
126. ↑ Internal fluctuations in a model of chemical chaos
127. ↑ "Main Page - Weigel's Research and Teaching Page". http://aurora.gmu.edu/projects/index.php?title=Main_Page.
128. ↑ Synchronization of Chaotic Fractional-Order WINDMI Systems via Linear State Error Feedback Control
129. ↑ Vaidyanathan, S.; Volos, Ch. K.; Rajagopal, K.; Kyprianidis, I. M.; Stouboulos, I. N. (2015). "Adaptive Backstepping Controller Design for the Anti-Synchronization of Identical WINDMI Chaotic Systems with Unknown Parameters and its SPICE Implementation". Journal of Engineering Science and Technology Review 8 (2): 74–82. doi:10.25103/jestr.082.11. http://www.jestr.org/downloads/Volume8Issue2/fulltext82112015.pdf.
130. ↑ 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. doi:10.1142/S0218127416501261. Bibcode: 2016IJBC...2650126C.

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Chaos theory

Chaos theory|

* Anosov diffeomorphism
* Bifurcation theory
* Butterfly effect
* Chaos theory in organizational development
* Complexity
* Control of chaos
* Dynamical system
* Edge of chaos
* Fractal
* Predictability
* Quantum chaos
* Santa Fe Institute
* Synchronization of chaos
* Unintended consequences

Chaotic maps
(list)|

* Arnold tongue
* Arnold's cat map
* Baker's map
* Complex quadratic map
* Complex squaring map
* Coupled map lattice
* Double pendulum
* Double scroll attractor
* Duffing equation
* Duffing map
* Dyadic transformation
* Dynamical billiards
* outer
* Elastic pendulum
* Exponential map
* Gauss map
* Gingerbreadman map
* Hénon map
* Horseshoe map
* Ikeda map
* Interval exchange map
* Kaplan–Yorke map
* Logistic map
* Lorenz system
* Multiscroll attractor
* Rabinovich–Fabrikant equations
* Rössler attractor
* Standard map
* Swinging Atwood's machine
* Tent map
* Three-body problem
* Tinkerbell map
* Van der Pol oscillator
* Zaslavskii map

Chaos systems|

* Bouncing ball dynamics
* Chua's circuit
* Economic bubble
* FPUT problem
* Tilt-A-Whirl

Chaos theorists|

* Michael Berry
* Mary Cartwright
* Leon O. Chua
* Mitchell Feigenbaum
* 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
* Mary Rees
* Otto Rössler
* David Ruelle
* Caroline Series
* Oleksandr Mykolayovych Sharkovsky
* Nina Snaith
* Floris Takens
* Audrey Terras
* Mary Tsingou
* Amie Wilkinson
* James A. Yorke
* Lai-Sang Young

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