FRACTAL ASPECTS OF THE ITERATION OF z →Λz(1‐ z) FOR COMPLEX Λ AND z

Citing Literature
Number of times cited: 111
- Predrag Cvitanović, Part 9 References, Universality in Chaos, 10.1201/9780203734636-50, (609-632), (2017).
- Michael Batty, Cities in Disequilibrium, Non-Equilibrium Social Science and Policy, 10.1007/978-3-319-42424-8_6, (81-96), (2017).
- J. Galeotti, K. Macdonald, J. Wang, S. Horvath, A. Zhang and R. Klatzky, Generating an image that affords slant perception from stereo, without pictorial cues, Displays, 46, (16), (2017).
- Yasmin Omar, Investigation of the Quaternion Dynamical System, Journal of Applied Mathematics and Physics, 05, 01, (131), (2017).
- R. Jones, R.K. Singh Raman and A.J. McMillan, Crack growth: Does microstructure play a role?, Engineering Fracture Mechanics, (2017).
- V.A. Chouliaras, D. Stevens and V.M. Dwyer, VThreads: A novel VLIW chip multiprocessor with hardware-assisted PThreads, Microprocessors and Microsystems, 47, (466), (2016).
- Romain Grandchamp and Arnaud Delorme, The Brainarium: An Interactive Immersive Tool for Brain Education, Art, and Neurotherapy, Computational Intelligence and Neuroscience, 2016, (1), (2016).
- Thomas Schmickl, Martin Stefanec and Karl Crailsheim, How a life-like system emerges from a simplistic particle motion law, Scientific Reports, 10.1038/srep37969, 6, 1, (2016).
- L. Hernandez Mengesha and C. J. James-Reynolds, Interactive Evolutionary Generative Art, Research and Development in Intelligent Systems XXXIII, 10.1007/978-3-319-47175-4_28, (377-382), (2016).
- Theodore Kim, Quaternion Julia Set Shape Optimization, Computer Graphics Forum, 34, 5, (167-176), (2015). 2015 20th Asia and South Pacific Design Automation Conference (ASP-DAC) Chiba, Japan The 20th Asia and South Pacific Design Automation Conference IEEE , (2015). 978-1-4799-7792-5 Guantao Liu, Tim Schmidt, Rainer Domer, Ajit Dingankar and Desmond Kirkpatrick Optimizing thread-to-core mapping on manycore platforms with distributed Tag Directories , (2015). 429 434 7059044 , 10.1109/ASPDAC.2015.7059044 http://ieeexplore.ieee.org/document/7059044/
- Francis Lacan and Charles Tresser, Fractals as objects with nontrivial structures at all scales, Chaos, Solitons & Fractals, 75, (218), (2015).
- J. C. Sprott and Anda Xiong, Classifying and quantifying basins of attraction, Chaos: An Interdisciplinary Journal of Nonlinear Science, 25, 8, (083101), (2015). 2015 IEEE International Parallel and Distributed Processing Symposium (IPDPS) Hyderabad, India 2015 IEEE International Parallel and Distributed Processing Symposium IEEE , (2015). 978-1-4799-8649-1 Aras Atalar, Anders Gidenstam, Paul Renaud-Goud and Philippas Tsigas Modeling Energy Consumption of Lock-Free Queue Implementations , (2015). 229 238 7161512 , 10.1109/IPDPS.2015.31 http://ieeexplore.ieee.org/document/7161512/
- Ya. Kononov and A. Morozov, Colored HOMFLY and generalized Mandelbrot set, Journal of High Energy Physics, 2015, 11, (2015).
- Cheng Zhang, Cycles of the Logistic Map, International Journal of Bifurcation and Chaos, 24, 01, (1450005), (2014).
- Shrihari Sridharan, Spectral Triple and Sinai–Ruelle–Bowen Measures, Complex Analysis and Operator Theory, 8, 7, (1513), (2014).
- Michel Steuwer and Sergei Gorlatch, SkelCL: a high-level extension of OpenCL for multi-GPU systems, The Journal of Supercomputing, 69, 1, (25), (2014).
- Mustafa Gökhan Benli, Rostislav Grigorchuk and Pierre de la Harpe, Amenable groups without finitely presented amenable covers, Bulletin of Mathematical Sciences, 10.1007/s13373-013-0031-5, 3, 1, (73-131), (2013).
- NIKOS KALOGEROPOULOS, TSALLIS ENTROPY COMPOSITION AND THE HEISENBERG GROUP, International Journal of Geometric Methods in Modern Physics, 10, 07, (1350032), (2013).
- Chao Wang, Wan-Ting Xiong and You-Gui Wang, Self-Similarity in Game-Locked Aggregation, Chinese Physics Letters, 29, 12, (128903), (2012).
- Gerardo Pastor, Miguel Romera, Amalia Beatriz Orue, Agustin Martin, Marius F. Danca and Fausto Montoya, Harmonic Analysis in Discrete Dynamical Systems, International Journal of Modern Nonlinear Theory and Application, 01, 01, (14), (2012).
- Elizabeth R. Chen, Mandelbrot Set + Symmetry Groups ∗ Higher Dimensions = ?, Discrete & Computational Geometry, (2012).
- YI-CHIUAN CHEN, TOMOKI KAWAHIRA, HUA-LUN LI and JUAN-MING YUAN, FAMILY OF INVARIANT CANTOR SETS AS ORBITS OF DIFFERENTIAL EQUATIONS II: JULIA SETS, International Journal of Bifurcation and Chaos, 21, 01, (77), (2011). Distributed Processing, Workshops and Phd Forum (IPDPSW) Anchorage, AK, USA 2011 IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum IEEE , (2011). 978-1-61284-425-1 Michel Steuwer, Philipp Kegel and Sergei Gorlatch SkelCL - A Portable Skeleton Library for High-Level GPU Programming , (2011). 1176 1182 6008967 , 10.1109/IPDPS.2011.269 http://ieeexplore.ieee.org/document/6008967/
- Sam Cole, Alliterative logic: A theory for postnormal times, Futures, 43, 2, (209), (2011).
- Archana Nigrawal and Navin Chand, Development and electrical characterization of carbon soot filled polyester graded composites, Materials & Design, 31, 8, (3672), (2010).
- Sébastien Clesse, Christophe Ringeval and Jonathan Rocher, Fractal initial conditions and natural parameter values in hybrid inflation, Physical Review D, 80, 12, (2009).
- Jacobo Aguirre, Ricardo L. Viana and Miguel A. F. Sanjuán, Fractal structures in nonlinear dynamics, Reviews of Modern Physics, 10.1103/RevModPhys.81.333, 81, 1, (333-386), (2009).
- G. Pastor, M. Romera, G. Alvarez, D. Arroyo, A.B. Orue, V. Fernandez and F. Montoya, A general view of pseudoharmonics and pseudoantiharmonics to calculate external arguments of Douady and Hubbard, Applied Mathematics and Computation, 213, 2, (484), (2009).
- Shrihari Sridharan, Rates of recurrence for real extensions of complex dynamics, Journal of Interdisciplinary Mathematics, 10.1080/09720502.2008.10700587, 11, 5, (617-627), (2008).
- Christos Skiadas and Charilaos Skiadas, References, Chaotic Modelling and Simulation, 10.1201/9781420079012.bmatt, (303-344), (2010).
- Ashish Negi and Mamta Rani, Midgets of superior Mandelbrot set, Chaos, Solitons & Fractals, 36, 2, (237), (2008).
- Wang Xingyuan and Zhang Xu, The divisor periodic point of escape-time N of the Mandelbrot set, Applied Mathematics and Computation, 187, 2, (1552), (2007).
- S. Sridharan, A counting result on two-dimension with error terms, Complex Variables and Elliptic Equations, 10.1080/17476930701228626, 52, 6, (485-494), (2007).
- G. Pastor, M. Romera, G. Álvarez, D. Arroyo and F. Montoya, On periodic and chaotic regions in the Mandelbrot set, Chaos, Solitons & Fractals, 32, 1, (15), (2007).
- Marco Camesasca, Miron Kaufman and Ica Manas-Zloczower, Staggered passive micromixers with fractal surface patterning, Journal of Micromechanics and Microengineering, 16, 11, (2298), (2006).
- Shrihari Sridharan, Non-vanishing derivatives of Lyapunov exponents and the pressure function, Dynamical Systems, 21, 4, (491), (2006).
- Lars Andersson, On the relation between mathematical and numerical relativity, Classical and Quantum Gravity, 23, 16, (S307), (2006).
- Ming-Chang Huang, Yu-Pin Luo and Tsong-Ming Liaw, Self-similar structure in the distribution and density of the partition function zeros, Physics Letters A, 320, 2-3, (180), (2003).
- Benoit B. Mandelbrot and Michael Frame, Fractals, Encyclopedia of Physical Science and Technology, 10.1016/B0-12-227410-5/00259-3, (185-207), (2003).
- G. Pastor, M. Romera, G. Álvarez and F. Montoya, How to work with one-dimensional quadratic maps, Chaos, Solitons & Fractals, 18, 5, (899), (2003).
- Sy-Sang Liaw, Parameter space of one-parameter complex mappings, Chaos, Solitons & Fractals, 13, 4, (761), (2002).
- SY-SANG LIAW, FIND THE MANDELBROT-LIKE SETS IN ANY MAPPING, Fractals, 10, 02, (137), (2002).
- WALTER BUCHANAN, JAGANNATHAN GOMATAM and BONNIE STEVES, GENERALIZED MANDELBROT SETS FOR MEROMORPHIC COMPLEX AND QUATERNIONIC MAPS, International Journal of Bifurcation and Chaos, 12, 08, (1755), (2002).
- Eugeniusz Majewski, Thermodynamics of Chaos and Fractals Applied: Evolution of the Earth and Phase Transformations, Earthquake Thermodynamics and Phase Transformations in the Earth's Interior, 10.1016/S0074-6142(01)80078-4, (25-80), (2001).
- M Romera, G Pastor, G Alvarez and F Montoya, Growth in complex exponential dynamics, Computers & Graphics, 24, 1, (115), (2000).
- Rafiqul Gani, Ian Cameron, Angelo Lucia, Gürkan Sin and Michael Georgiadis, Process Systems Engineering, 2. Modeling and Simulation, Ullmann's Encyclopedia of Industrial Chemistry, (2012).
- G. P. KAPOOR and M. GURU PREM PRASAD, CHAOTIC BURST IN THE DYNAMICS OF A CLASS OF NONCRITICALLY FINITE ENTIRE FUNCTIONS, International Journal of Bifurcation and Chaos, 09, 06, (1137), (1999).
- Alan Norton, Julia sets in the quaternions, Chaos and Fractals, 10.1016/B978-044450002-1/50038-2, (235-246), (1998).
- Michael Michelitsch and Otto E. Rössler, The “burning ship” and its quasi-Julia sets, Chaos and Fractals, 10.1016/B978-044450002-1/50048-5, (287-290), (1998).
- Michael Michelitsch, Color maps generated by “trigonometric iteration loops”, Chaos and Fractals, 10.1016/B978-044450002-1/50040-0, (251-252), (1998).
- Michael Klein, Otto E. Rössler, Jürgen Paris, Joachim Peinke, Gerold Baier, Claus Kahlert and John L. Hudson, Toward a better understanding of fractality in nature, Chaos and Fractals, 10.1016/B978-044450002-1/50016-3, (79-92), (1998).
- Curtis T. McMullen and Dennis P. Sullivan, Quasiconformal Homeomorphisms and Dynamics III. The Teichmüller Space of a Holomorphic Dynamical System, Advances in Mathematics, 135, 2, (351), (1998).
- M.P. Deseilligny, G. Stamon and Ching Y. Suen, Veinerization: a new shape description for flexible skeletonization, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20, 5, (505), (1998).
- J.Andrew Gitter and M.Joseph Czerniecki, Fractal analysis of the electromyographic interference pattern, Journal of Neuroscience Methods, 58, 1-2, (103), (1995).
- Jagannathan Gomatam, John Doyle, Bonnie Steves and Isobel McFarlane, Generalization of the Mandelbrot set: Quaternionic quadratic maps, Chaos, Solitons & Fractals, 5, 6, (971), (1995).
- John Stephenson, Spirals in the Mandelbrot set I, Physica A: Statistical Mechanics and its Applications, 205, 4, (634), (1994).
- James B. Bassingthwaighte and Gary M. Raymond, Evaluating rescaled range analysis for time series, Annals of Biomedical Engineering, 22, 4, (432), (1994).
- Norbert Steinmetz, Bibliography, Rational Iteration, 10.1515/9783110889314.183, (1993).
- P. Hamilton, A language to describe the growth of neurites, Biological Cybernetics, 68, 6, (559), (1993).
- Angelo Lucia, Xinzhou Guo and Xiaofeng Wang, Process simulation in the complex domain, AIChE Journal, 39, 3, (461-470), (2004).
- John Stephenson and Douglas T. Ridgway, Formulae for cycles in the Mandelbrot set II, Physica A: Statistical Mechanics and its Applications, 190, 1-2, (104), (1992).
- Michael Michelitsch and Otto E. Rössler, The “burning ship” and its quasi-Julia sets, Computers & Graphics, 16, 4, (435), (1992).
- John Stephenson, Formulae for cycles in the Maldelbrot set III, Physica A: Statistical Mechanics and its Applications, 190, 1-2, (117), (1992).
- John R. Tippetts, A simple algorithm giving an interesting Mandelbrot set, The Visual Computer, 8, 3, (200), (1992).
- , Bibliography, , 10.1016/S0049-237X(08)70025-9, (603-641), (1992).
- John Stephenson, Formulae for cycles in the Mandelbrot set, Physica A: Statistical Mechanics and its Applications, 177, 1-3, (416), (1991).
- Michael Klein, Otto E. Rössler, Jürgen Parisi, Joachim Peinke, Gerold Baier, Claus Kahlert and John L. Hudson, Toward a better understanding of fractality in nature, Computers & Graphics, 15, 4, (583), (1991).
- Angelo Lucia, Xinzhou Guo, Paula J. Richey and Ramnath Derebail, Simple process equations, fixed‐point methods, and chaos, AIChE Journal, 36, 5, (641-654), (2004).
- Michael Michelitsch, Color maps generated by “trigonometric iteration loops”, Computers & Graphics, 14, 1, (125), (1990).
- Jeffrey E. Arle and Richard H. Simon, An application of fractal dimension to the detection of transients in the electroencephalogram, Electroencephalography and Clinical Neurophysiology, 75, 4, (296), (1990).
- Jean-Luc Chabert, Un demi-siecle de fractales: 1870–1920, Historia Mathematica, 17, 4, (339), (1990). First IEEE Conference on Visualization: Visualization `90 San Francisco, CA, USA 23-26 Oct. 1990 Proceedings of the First IEEE Conference on Visualization: Visualization `90 IEEE Comput. Soc. Press , (1990). 0-8186-2083-8 J.C. Hart, L.H. Kauffman and D.J. Sandim Interactive visualization of quaternion Julia sets 209 218, , 10.1109/VISUAL.1990.146384 http://ieeexplore.ieee.org/document/146384/ 1990 IJCNN International Joint Conference on Neural Networks San Diego, CA, USA 1990 IJCNN International Joint Conference on Neural Networks IEEE , (1990). T.L. Clarke Generalization of neural networks to the complex plane , (1990). 435 440 vol.2 5726710 , 10.1109/IJCNN.1990.137751 http://ieeexplore.ieee.org/document/5726710/
- Predrag Cvitanović and Jan Myrheim, Complex universality, Communications in Mathematical Physics, 121, 2, (225), (1989).
- E. Hornbogen, Fractals in microstructure of metals, International Materials Reviews, 34, 1, (277), (1989).
- Alan Norton, Julia sets in the quaternions, Computers & Graphics, 13, 2, (267), (1989).
- Bruce Elenbogen and Thomas Kaeding, A weak estimate of the fractal dimension of the Mandelbrot boundary, Physics Letters A, 136, 7-8, (358), (1989).
- Ian R. Price and Robert A. M. Gregson, Nonlinear dynamics in a complex cubic one-dimensional model for sensory psychophysics, Acta Applicandae Mathematicae, 11, 1, (1), (1988).
- S Bullett, Dynamics of quadratic correspondences, Nonlinearity, 1, 1, (27), (1988).
- F. v. Haeseler and H. O. Peitgen, Newton's method and complex dynamical systems, Acta Applicandae Mathematicae, 13, 1-2, (3), (1988).
- ARNOLD J. MANDELL, PATRICK V. RUSSO and BARBARA W. BLOMGREN, Geometric Universality in Brain Allosteric Protein Dynamics:, Annals of the New York Academy of Sciences, 504, 1, (88-117), (2006).
- Edward R. Vrscay and William J. Gilbert, Extraneous fixed points, basin boundaries and chaotic dynamics for Schr�der and K�nig rational iteration functions, Numerische Mathematik, 52, 1, (1), (1987).
- Mogens H. Jensen, Leo P. Kadanoff and Itamar Procaccia, Scaling structure and thermodynamics of strange sets, Physical Review A, 36, 3, (1409), (1987).
- R. Delbourgo, P. Hughes and B. G. Kenny, Islands of stability and complex universality relations, Journal of Mathematical Physics, 28, 1, (60), (1987).
- E R Vrscay, Mandelbrot sets for pairs of affine transformations in the plane, Journal of Physics A: Mathematical and General, 19, 11, (1985), (1986).
- Paul Blanchard, DISCONNECTED JULIA SETS, Chaotic Dynamics and Fractals, 10.1016/B978-0-12-079060-9.50016-3, (181-201), (1986).
- Michael F. Barnsley, MAKING CHAOTIC DYNAMICAL SYSTEMS TO ORDER, Chaotic Dynamics and Fractals, 10.1016/B978-0-12-079060-9.50008-4, (53-68), (1986).
- Pierre Moussa, DIOPHANTINE PROPERTIES OF JULIA SETS, Chaotic Dynamics and Fractals, 10.1016/B978-0-12-079060-9.50018-7, (215-227), (1986).
- Predrag CVITANOVIĆ, Mogens H. JENSEN, Leo P. KADANOFF and Itamar PROCACCIA, CIRCLE MAPS IN THE COMPLEX PLANE, Fractals in Physics, 10.1016/B978-0-444-86995-1.50081-0, (439-445), (1986).
- Arun V. Holden, Frontiers of chaos, Physica D: Nonlinear Phenomena, 19, 2, (307), (1986).
- G. C. Martínez-Mekler, Raúl Mondragón and Rafael Pérez, Basin-structure invariance of circle maps with bistable dynamics, Physical Review A, 33, 3, (2143), (1986).
- Peter H. Richter and Heinz‐Otto Peitgen, Morphology of Complex Boundaries, Berichte der Bunsengesellschaft für physikalische Chemie, 89, 6, (571-588), (2010).
- M.F. Barnsley and A.N. Harrington, A mandelbrot set for pairs of linear maps, Physica D: Nonlinear Phenomena, 15, 3, (421), (1985).
- Heinz-Otto Peitgen and Peter H. Richter, The mandelbrot set in a model for phase transitions, Arbeitstagung Bonn 1984, 10.1007/BFb0084587, (111-135), (2006).
- Predrag Cvitanović, Mogens H. Jensen, Leo P. Kadanoff and Itamar Procaccia, Renormalization, unstable manifolds, and the fractal structure of mode locking, Physical Review Letters, 55, 4, (343), (1985).
- Feliks Przytycki, Hausdorff dimension of harmonic measure on the boundary of an attractive basin for a holomorphic map, Inventiones Mathematicae, 80, 1, (161), (1985).
- B W Southern and P D Loly, A rescaling approach to two- and three-dimensional lattice spectra, Journal of Physics A: Mathematical and General, 18, 3, (525), (1985).
- Steven W. McDonald, Celso Grebogi, Edward Ott and James A. Yorke, Fractal basin boundaries, Physica D: Nonlinear Phenomena, 10.1016/0167-2789(85)90001-6, 17, 2, (125-153), (1985).
- John Miles, Strange Attractors in Fluid Dynamics, Advances in Applied Mechanics Volume 24, 10.1016/S0065-2156(08)70045-0, (189-214), (1984).
- Robert L. Devaney, Bursts into chaos, Physics Letters A, 104, 8, (385), (1984).
- D. Bessis, J. S. Geronimo and P. Moussa, Meblin transforms associated with Julia sets and physical applications, Journal of Statistical Physics, 34, 1-2, (75), (1984).
- J.P. Clerc, A.-M.S. Tremblay, G. Albinet and C.D. Mitescu, a.c. response of fractal networks, Journal de Physique Lettres, 45, 19, (913), (1984).
- Michael Widom, David Bensimon, Leo P. Kadanoff and Scott J. Shenker, Strange objects in the complex plane, Journal of Statistical Physics, 32, 3, (443), (1983).
- M. F. Barnsley, J. S. Geronimo and A. N. Harrington, On the invariant sets of a family of quadratic maps, Communications in Mathematical Physics, 88, 4, (479), (1983).
- J. -M. Langlois, A. -M. Tremblay and B. W. Southern, Chaotic scaling trajectories and hierarchical lattice models of disordered binary harmonic chains, Physical Review B, 28, 1, (218), (1983).
- A.-M.S. Tremblay and B.W. Southern, Scaling and density of states of fractal lattices from a generating function point of view, Journal de Physique Lettres, 44, 20, (843), (1983).
- N. S. Manton and M. Nauenberg, Universal scaling behaviour for iterated maps in the complex plane, Communications in Mathematical Physics, 89, 4, (555), (1983).
- Predrag Cvitanović and Jan Myrheim, Universality for period n-tuplings in complex mappings, Physics Letters A, 94, 8, (329), (1983).
- David Ruelle, Repellers for real analytic maps, Ergodic Theory and Dynamical Systems, 2, 01, (99), (1982).




