Chaos theory | Fractals | Dimension theory | Dynamical systems
Fractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset, or a pattern or signal extracted from phenomena including topography, natural geometric objects, ecology and aquatic sciences, sound, market fluctuations, heart rates, frequency domain in electroencephalography signals, digital images, molecular motion, and data science. Fractal analysis is now widely used in all areas of science. An important limitation of fractal analysis is that arriving at an empirically determined fractal dimension does not necessarily prove that a pattern is fractal; rather, other essential characteristics have to be considered. Fractal analysis is valuable in expanding our knowledge of the structure and function of various systems, and as a potential tool to mathematically assess novel areas of study. was formulated which is a generalization of ordinary calculus (Wikipedia).
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From playlist research
Summer of math exposition submission- fractal calculus
Fractal Calculus
From playlist Summer of Math Exposition Youtube Videos
In this video, I define a neat concept called the fractal derivative (which shouldn't be confused with fractional derivatives). Then I provide a couple of examples, and finally I present an application of this concept to the study of anomalous diffusion in physics. Enjoy!
From playlist Calculus
mandelbrot fractal animation 5
another mandelbrot/julia fractal animation/morph.
From playlist Fractal
Fractals are typically not self-similar
An explanation of fractal dimension. Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: https://3b1b.co/fractals-thanks And by Affirm: https://www.affirm.com/careers H
From playlist Explainers
The Newton Fractal Explained | Deep Dive Maths
A Newton fractal is obtained by iterating Newton's method to find the roots of a complex function. The iconic picture of this fractal is what I call The Newton Fractal, and is generated from the function f(z)=z^3-1, whose roots are the three cube roots of unity. What is the history of th
From playlist Deep Dive Maths
Alain Arneodo: Wavelet-based multifractal analysis of dynamic infrared thermograms [...]
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist 30 years of wavelets
Semiclassical analysis, chaotic dynamics, and fractal uncertainty principle - Semyon Dyatlov
Emerging Topics Working Group Topic: Semiclassical analysis, chaotic dynamics, and fractal uncertainty principle Speaker: Semyon Dyatlov Affiliation: Massachusetts Institute of Technology Date: October 10, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Musimathics: Fractals & Self-Similarity (Part 10)
Welcome to the Musimathics series! Musimathics gives an overview of some of the most interesting topics in the field of mathematical music theory! You are watching the tenth video in the series. In this video, Chloe goes over the basics of fractals and self-similarity, as well as their ap
From playlist Musimathics: Music & Math
Additive Energy of Regular Measures in One and Higher Dimensions, and the Fractal... - Laura Cladek
Analysis & Mathematical Physics Topic: Additive Energy of Regular Measures in One and Higher Dimensions, and the Fractal Uncertainty Principle Speaker: Laura Cladek Affiliation: von Neumann Fellow, School Of Mathematics Date: December 14, 2022 We obtain new bounds on the additive energy
From playlist Mathematics
Real Analysis Ep 17: The Cantor Set
Episode 17 of my videos for my undergraduate Real Analysis course at Fairfield University. This is a recording of a live class. This episode is about the Cantor set. Class webpage: http://cstaecker.fairfield.edu/~cstaecker/courses/2020f3371/ Chris Staecker webpage: http://faculty.fairfie
From playlist Math 3371 (Real analysis) Fall 2020
Householder's Method for finding roots of equations including history, derivation, examples, and fractals. Example code is available on GitHub https://github.com/osveliz/numerical-veliz Chapters 0:00 Intro 0:25 Derivation 1:58 History 2:34 Householder's Method 4:07 Householder's Method Ex
From playlist Root Finding
Asymptotic Analysis of Spectral Problems in Thick Junctions with the Branched...by Taras Mel’nyk
DISCUSSION MEETING Multi-Scale Analysis: Thematic Lectures and Meeting (MATHLEC-2021, ONLINE) ORGANIZERS: Patrizia Donato (University of Rouen Normandie, France), Antonio Gaudiello (Università degli Studi di Napoli Federico II, Italy), Editha Jose (University of the Philippines Los Baño
From playlist Multi-scale Analysis: Thematic Lectures And Meeting (MATHLEC-2021) (ONLINE)
Time Series Analysis of Terrorist events in the Global Terrorism Database by Sunil Kumar
Program Summer Research Program on Dynamics of Complex Systems ORGANIZERS: Amit Apte, Soumitro Banerjee, Pranay Goel, Partha Guha, Neelima Gupte, Govindan Rangarajan and Somdatta Sinha DATE : 15 May 2019 to 12 July 2019 VENUE : Madhava hall for Summer School & Ramanujan hall f
From playlist Summer Research Program On Dynamics Of Complex Systems 2019
This shows a 3d print of a mathematical sculpture I produced using shapeways.com. This model is available at http://shpws.me/8wEX
From playlist 3D printing
Fractal uncertainty principle and its applications - Semyon Dyatlov
Emerging Topics Working Group Topic:Fractal uncertainty principle and its applications Speaker: Semyon Dyatlov Affiliation: Massachusetts Institute of Technology Date: October 9, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
What are fractals? Just look at your broccoli to find out! License: Creative Commons BY-NC-SA More information at http://k12videos.mit.edu/terms-conditions
From playlist Measurement
Maryna Kachanovska: Transparent boundary conditions for wave propagation in fractal trees
CONFERENCE Recorded during the meeting " Herglotz-Nevanlinna Functions and their Applications to Dispersive Systems and Composite Materials " the May 25, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video a
From playlist Mathematics in Science & Technology