Concept

Fractal dimension

Related lectures (32)

Explores chaotic maps, fractal dimensions, and strange attractors in dynamical systems.

Delves into complex systems, strange attractors, and epidemics, emphasizing the influence of psychological factors and the role of contagion.

Fractals: Dimensions and Applications

Explores fractals, dimensions, and applications, including mountain formation simulation and landscape authoring through erosion and vegetation interplay.

Nonlinear Dynamics: Chaos and Complex Systems

Explores countable and uncountable sets, Cantor set, Mandelbrot set, and Box dimension in nonlinear dynamics and complex systems.

Chaos Theory: Fractals and Dimensionality

Explores chaotic systems, fractals, and dimensions in Chaos Theory.

FK-Percolation and the Six-Vertex Model: Critical Phenomena

Covers the transition from the six-vertex model to FK-percolation, focusing on critical phenomena and phase transitions in two-dimensional systems.

Fractal Dimensions: Polymer Behavior

Explores fractal dimensions in polymer behavior, focusing on excluded volume and intersections within polymers.

Nonlinear Dynamics and Complex Systems

Covers chaotic behavior in complex systems, with applications in various fields and a historical overview of major developments in chaos theory.

Bifurcation and fractals in complex dynamical systems

Explores bifurcation, fractals, Julia sets, Mandelbrot set, and self-similarity in complex dynamical systems.

Intermittency and Corrections to Kolmogorov Theory

Explores intermittency and corrections to the Kolmogorov theory based on data deviations and assumptions violations.

End-to-End Distance Exponent

Explores the correct exponent for the end-to-end distance in polymer chains and its implications on chain correlations.

Roulette with Curves and Surfaces

Explores building a roulette, probability distributions on curves, and properties of random surface models, including the groundbreaking Schramm-Loewner evolution processes.

Turbulent State Symmetries

Explores broken and emerging symmetries in turbulent states, discussing energy cascades, lack of scale invariance, and potential conformal invariance.

Fractal Dimension: Understanding Complex Geometric Structures

Explores fractal dimension, calculating values analytically and providing practical examples in computer graphics.

Procedural Models: L-Systems

Explores procedural models, focusing on L-systems to generate intricate graphical patterns resembling natural structures.

Fractals and Strange Attractors

Delves into renormalization, fractals, and strange attractors, exploring the properties of countable and uncountable sets.

Chaos Theory: Chaotic Maps and Logistic Map

Explores chaotic maps, fix points, periodic orbits, and intermittent chaos.

Chaos Theory: Discrete Dynamical Systems

Explores Chaos Theory through Discrete Dynamical Systems and the Arnold's Cat Map.

Project Organization & Intro

Introduces the PONG Project in Digital System Design, focusing on developing a custom digital circuit for a PONG game with a Mandelbrot background.

Chaos Theory: Maps and Lyapunov Exponents

Explores chaotic maps, fix points, stability, and Lyapunov exponents in discrete systems, emphasizing their role in determining chaos.