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#Fractal Geometry

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University of Oxford

The Butterfly Effect - What Does It Really Signify?

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Explore chaos theory, determinism, and unpredictability through the lens of Ed Lorenz's work and the true meaning of the Butterfly Effect in meteorology and climate physics.
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24 Lesons
1 hour 1 minute
On-Demand
Free-Video
Institute for Pure & Applied Mathematics (IPAM)

Geometric Representations of Far Future Predictions in Deep Neural Networks - Next-Token Training

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Explore universal geometric representations of far-future beliefs in deep neural networks trained on next-token prediction, uncovering fractal and quantum-like structures embedded in network activations.
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1 Lesons
54 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Integral Means Spectrum: Examples of Exact Computation

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Explore the multifractal spectrum of harmonic measure and integral-means spectrum of Riemann maps through explicit computations in deterministic and random cases.
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1 Lesons
1 hour 32 minutes
On-Demand
Free-Video
3Blue1Brown

Fractals Are Typically Not Self-Similar

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Explore fractal dimension, self-similarity, and scaling in this engaging explanation that challenges common misconceptions about fractals and their properties.
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5 Lesons
22 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

On Dynamics of Lorenz Maps - Renormalizations and Invariant Sets

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Explore the dynamics of Lorenz maps, focusing on renormalizations and invariant sets. Delve into piecewise monotone interval maps, their connections to number theory, and fractal geometry.
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1 Lesons
54 minutes
On-Demand
Free-Video
Institute for Advanced Study

Insights into the Geometric Harmonic Analysis Associated to 1-Parameter Sets

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Explore geometric harmonic analysis of 1-parameter sets with insights from D. Dominique Kemp's research at the Institute for Advanced Study.
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1 Lesons
22 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Self-affine Systems and Hausdorff Dimension Theory - Lecture 1B

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Delve into the dimension theory of self-affine systems, exploring Falconer's foundational work and recent advances in calculating Hausdorff dimensions of planar self-affine sets.
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1 Lesons
44 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Self-affine Systems and Iterated Function Systems - Lecture 1A

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Explore the dimension theory of iterated function systems, focusing on non-conformal transformations and the calculation of Hausdorff dimension in planar self-affine sets.
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1 Lesons
45 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Estimating Dimension and Lyapunov Exponents - Lecture 1B

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Delve into advanced mathematical concepts exploring Hausdorff dimensions, Lyapunov exponents, and their applications to number theory and geometric systems through conformal iterated function schemes.
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1 Lesons
1 hour 2 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Self-affine Systems and Hausdorff Dimension Theory - Lecture 2A

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Delve into the dimension theory of self-affine systems, exploring Hausdorff dimensions, Falconer's results, and recent developments in non-conformal transformations and planar self-affine sets.
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1 Lesons
45 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Self-affine Systems and Hausdorff Dimension Theory - Lecture 2B

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Delve into the dimension theory of self-affine systems, exploring Hausdorff dimensions, Falconer's results, and recent developments in non-conformal transformations and planar self-affine sets.
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1 Lesons
50 minutes
On-Demand
Free-Video
International Mathematical Union

Self-Similar Sets and Measures on the Line

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Explore fractal geometry through self-similar sets and measures, focusing on recent developments in determining their dimensions. Gain insights into classical fractals and cutting-edge research.
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10 Lesons
49 minutes
On-Demand
Free-Video
Hausdorff Center for Mathematics

Osama Khalil- Diophantine Approximation on Fractals and Homogeneous Flows

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Explore Diophantine approximation on fractals and homogeneous flows, examining exceptional sets and their connections to recurrence behavior. Discover new results on Hausdorff dimension of divergent orbits and self-similar measure projections.
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1 Lesons
48 minutes
On-Demand
Free-Video
The Royal Institution

Chaos Theory and Geometry - Can They Predict Our World? With Tim Palmer

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Explore chaos theory's geometry to predict uncertain phenomena like weather, pandemics, and quantum physics. Discover insights into the universe and ourselves through fractal patterns and probabilistic approaches.
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15 Lesons
1 hour 10 minutes
On-Demand
Free-Video
AGU

Fractals and Multifractals in Geophysics - Lorenz Lecture

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Explore fractals and their applications in geophysics with renowned mathematician Benoit Mandelbrot in this historic AGU Fall Meeting lecture from 2001.
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1 Lesons
1 hour 9 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Topological and Conformal Dimensions of Self-Similar Groups

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Explore topological and conformal dimensions of self-similar groups, examining their limit spaces and associated dynamical systems in geometric group theory.
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1 Lesons
50 minutes
On-Demand
Free-Video
Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

Dynamical Subsets in Iterated Function Systems

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Explore dynamical subsets in iterated function systems with Henna Koivusalo's in-depth analysis of rare events in dynamical systems.
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1 Lesons
54 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Harmonic Measure with Robin Boundary Conditions

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Explore harmonic measure with Robin boundary conditions in this mathematical analysis talk by Guy David at CIRM's thematic meeting on fractals and networks.
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1 Lesons
39 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Structure of Feigenbaum Henon Maps

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Explore Feigenbaum Henon maps structure in dynamical systems with Mikhail Lyubich's conference talk, part of a broad meeting celebrating Marcelo Viana's 60th birthday at IMPA.
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1 Lesons
56 minutes
On-Demand
Free-Video
Big Ideas In Dynamics

Thermodynamic Formalism and Conformal Iterated Function Systems

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Explore advanced concepts in dynamical systems, focusing on thermodynamic formalism and conformal iterated function systems.
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1 Lesons
1 hour 31 minutes
On-Demand
Free-Video
Conference GSI

On the Entropy of Rectifiable and Stratified Measures

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Explore entropy concepts for rectifiable and stratified measures, delving into mathematical intricacies and theoretical foundations.
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1 Lesons
23 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

Some Algebraic Tools in Fractal Geometry

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Explore algebraic tools in fractal geometry, focusing on open conjectures, random lattices, and volume estimates. Gain insights into Sato-Bernstein theory and zeta distributions.
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28 Lesons
59 minutes
On-Demand
Free-Video
Centre International de Rencontres Mathématiques

One-sided Multifractal Analysis of Gibbs Measures on the Line

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Explore one-sided multifractal analysis of Gibbs measures on the line. Delve into advanced mathematical concepts with De-Jun Feng's in-depth conference talk from the CIRM thematic meeting.
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1 Lesons
1 hour 3 minutes
On-Demand
Free-Video
Institut des Hautes Etudes Scientifiques (IHES)

Geometric Laplacians on Self-Conformal Fractal Curves in the Plane

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Explore geometric Laplacians on self-conformal fractal curves, examining heat kernels, eigenvalue asymptotics, and their relation to fractal geometry. Delve into construction methods and applications in complex analysis.
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1 Lesons
51 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Fractal Weyl Bounds

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Explore fractal Weyl bounds in spectral geometry with Anke Pohl, delving into advanced mathematical concepts and their applications.
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1 Lesons
1 hour 4 minutes
On-Demand
Free-Video
Centre de recherches mathématiques - CRM

Why p-adic Numbers Are Better Than Real for Representation Theory

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Explore p-adic numbers and their application in representation theory, focusing on SL(2) group and nilpotent orbits in Lie algebra.
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1 Lesons
58 minutes
On-Demand
Free-Video
BIMSA

Applications of Additive Combinatorics to Problems in Fractal Geometry

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Explore applications of additive combinatorics in fractal geometry, focusing on self-similar sets with overlaps and recent advancements in the field.
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1 Lesons
59 minutes
On-Demand
Free-Video
Banach Center

Estimating Hausdorff Dimension via Iterated Function Schemes

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Explore methods for estimating Hausdorff dimension using iterated function schemes, presented by Mark Pollicott from the University of Warwick.
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1 Lesons
57 minutes
On-Demand
Free-Video
Banach Center

Cantor Julia Sets

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Explore Cantor Julia sets and their mathematical properties through an in-depth analysis by Vyron Vellis from the University of Tennessee, Knoxville.
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1 Lesons
48 minutes
On-Demand
Free-Video
Banach Center

Indecomposable Continua in Exponential Dynamics

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Explore indecomposable continua in exponential dynamics, delving into advanced mathematical concepts and their applications.
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1 Lesons
39 minutes
On-Demand
Free-Video
Banach Center

The Mandelbrot Set and Its Satellite Copies

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Explore the fascinating world of the Mandelbrot set and its satellite copies, delving into complex mathematical concepts and intricate geometric patterns.
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1 Lesons
1 hour 1 minute
On-Demand
Free-Video
Banach Center

On a Mandelbrot-Like Set for a Family of Exponential Maps

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Explore the intricacies of Mandelbrot-like sets in exponential map families, delving into complex mathematical concepts and their applications.
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1 Lesons
26 minutes
On-Demand
Free-Video
Simons Semester on Dynamics

Recent Progress on Dimension Drop Conjecture

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Delve into recent advances in dimension drop conjecture, exploring self-similar sets, Hochman's theorem, and exponential separation in fractal geometry with applications to algebraic parameters.
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1 Lesons
1 hour 50 minutes
On-Demand
Free-Video
Envato Tuts+

Introduction to Vue 9 xStream - Fractal Landscapes and Terrain Generation - Part 3

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Learn to create intricate fractal landscapes in Vue, focusing on rocky mountains, terrain details, and advanced distortion techniques for realistic environments.
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14 Lesons
21 minutes
On-Demand
Free-Video
USC Probability and Statistics Seminar

Critical Behaviour in Hierarchical Percolation - Statistical Mechanics Models

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Explore critical behavior in hierarchical percolation, examining phase transitions, fractal-like patterns, and critical exponents across dimensions.
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1 Lesons
51 minutes
On-Demand
Free-Video
Teaching Tech

3D Printed Fractal Vise - The Coolest Tool You Didn't Know You Needed

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Learn to design, 3D print, and assemble a fractal vise - a versatile tool that can clamp objects of various shapes. Explore the concept, design process, printing tips, and assembly techniques.
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9 Lesons
15 minutes
On-Demand
Free-Video
Devoxx

The Art of Code

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Explore the intersection of coding and creativity, from Conway's Game of Life to esoteric languages and live coding performances, in this entertaining look at programming as an art form.
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27 Lesons
54 minutes
On-Demand
Free-Video
Isaac Newton Institute for Mathematical Sciences

The Mathematical Universe Behind Deep Neural Networks - Rothschild Lecture

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Explore the mathematical foundations of deep neural networks, covering functional analysis, harmonic analysis, complex analysis, approximation theory, and more with Professor Helmut Bölcskei.
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1 Lesons
1 hour 11 minutes
On-Demand
Free-Video
Instituto de Matemática Pura e Aplicada

Fractal Geometry of the Markov and Lagrange Spectra and Their Set Difference

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Delve into the fractal geometry of Markov and Lagrange spectra, exploring their set differences and mathematical properties through advanced number theory and geometric analysis.
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1 Lesons
1 hour 6 minutes
On-Demand
Free-Video