In mathematics, Lyapunov fractals (also known as Markus–Lyapunov fractals) are bifurcational fractals derived from an extension of the logistic map in which the degree of the growth of the population, r, periodically switches between two values A and B. A Lyapunov fractal is constructed by mapping the regions of stability and chaotic behaviour (measured using the Lyapunov exponent ) in the a−b plane for given periodic sequences of a and b. In the images, yellow corresponds to (stability), and blue corresponds to (chaos). Lyapunov fractals were discovered in the late 1980s by the Germano-Chilean physicist from the Max Planck Institute of Molecular Physiology. They were introduced to a large public by a science popularization article on recreational mathematics published in Scientific American in 1991. (Wikipedia).
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From playlist research
mandelbrot fractal animation 5
another mandelbrot/julia fractal animation/morph.
From playlist Fractal
Lyapunov's Fractal (that Lyapunov knew nothing about) #SoME2
Hi everyone! I hope you enjoy my first video. I've known about Markus-Lyapunov Fractals for a few years now, and it surprised me that I couldn't find any video explaining how they work - so I thought I'd take a stab at it myself! This is also my submission for Summer of Math Exposition 2.
From playlist Summer of Math Exposition 2 videos
On Bowen's equation for non-conformal repellers by Nuno Luzia
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
This Mandelbulb fractal is real!
A fractal just grew from my desk! Testing my Shadertoy plugin for After Effects ^_^
From playlist Shorts
A Toy Model for Time Evolving QFT on Lattice with Controllable Chaos by David Berenstein
Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography DATE:27 January 2018 to 03 February 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore The program "Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography" aims to
From playlist Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory and Holography
Machine learning analysis of chaos and vice versa - Edward Ott, University of Maryland
About the talk In this talk we first consider the situation where one is interested in gaining understanding of general dynamical properties of a chaotically time evolving system solely through access to time series measurements that depend on the evolving state of an, otherwise unknown,
From playlist Turing Seminars
Decimated Navier-Stokes turbulence by Samriddhi Sankar Ray
PROGRAM DYNAMICS OF COMPLEX SYSTEMS 2018 ORGANIZERS Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE: 16 June 2018 to 30 June 2018 VENUE: Ramanujan hall for Summer School held from 16 - 25 June, 2018; Madhava hall for W
From playlist Dynamics of Complex systems 2018
MAE5790-18 Strange attractor for the Lorenz equations
Defining attractor, chaos, and strange attractor. Transient chaos in games of chance. Dynamics on the Lorenz attractor. Reduction to a 1-D map: the Lorenz map. Ruling out stable limit cycles for the Lorenz system when r = 28. Cobweb diagrams. Reading: Strogatz, "Nonlinear Dynamics and Ch
From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University
Round table on open problems in non-equilibrium statistical physics... - Michael Aizenmann
Michael Aizenmann Princeton University March 28, 2014 For more videos, visit http://video.ias.edu
From playlist Mathematics
60 years of dynamics and number expansions - 14 December 2018
http://crm.sns.it/event/441/ 60 years of dynamics and number expansions Partially supported by Delft University of Technology, by Utrecht University and the University of Pisa It has been a little over sixty years since A. Renyi published his famous article on the dynamics of number expa
From playlist Centro di Ricerca Matematica Ennio De Giorgi
S. Skripchenko - Rauzy gasket, Arnoux-Yoccoz interval exchange map, Novikov's problem (Part 2)
1. Symbolic dynamics: Arnoux - Rauzy words and Rauzy gasket 2. Topology: Arnoux - Yoccoz example and its generalization 3. Novikov’s problem: how dynamics meets topology and together they help to physics 4. Lyapunov exponents for the Rauzy gasket: what do we know about them 5. Multidimensi
From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications
some julia dynamics combined with a rotation in the direction of mandelbrot.
From playlist Fractal
Thin monodromy and Lyapunov exponents, via Hodge theory - Simion Filip
Analysis Seminar Topic: Thin monodromy and Lyapunov exponents, via Hodge theory Speaker: Simion Filip Affiliation: Harvard University Date: November 15, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
From playlist Simulink Design Award: 2013 BEST Robotics