Limit sets | Fractals | Complex dynamics
In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values.Thus the behavior of the function on the Fatou set is "regular", while on the Julia set its behavior is "chaotic". The Julia set of a function f is commonly denoted and the Fatou set is denoted These sets are named after the French mathematicians Gaston Julia and Pierre Fatou whose work began the study of complex dynamics during the early 20th century. (Wikipedia).
Arrays can be used as sets, but Julia has a dedicated Set() function that eliminates any duplicate entries, proper for use in set theorey.
From playlist The Julia Computer Language
Julia Language Database JuliaDB
JuliaDB is Julia's own database structure. You can read more about it at http://juliadb.org The next few videos aim to make you familiar with this new package. So, if you want to use something more than just DataFrames, watch this space. In this first video, we take a look at the table
From playlist Julia on Coursera
In this video, I take a look at the Julia Statistics Package. It is installed with Julia and contains the functions that we use for summary statistics all the time: mean, median, standard deviation, and quantiles.
From playlist Julia on Coursera
Setting up Julia (using Juliabox.org) to import our dataset and start our data analysis.
From playlist The Julia Computer Language
From playlist mandelstir
In this second video on JuliaDB we take a look at how to create a new table from an existing one, but only including certain rows that fulfill a certain criteria. This is achieved using the filter function in Julia as well as an anonymous function. For a full course in Julia, have a look
From playlist Julia on Coursera
With dictionaries we create both a set of elements and specify a key for each. We can reference these keys instead of the usual indices wes used in arrays.
From playlist The Julia Computer Language
At times, it might be useful to express a single column in a table as a single value, such as adding all the values in that column or calculating the mean or variance of the values in that column. This can be achieved using the reduce() function. For a full course in Julia, have a look a
From playlist Julia on Coursera
Coding Challenge #22: Julia Set in Processing
In this coding challenge, I program the Julia Set fractal in Processing (Java). Code: https://thecodingtrain.com/challenges/22-julia-set 🕹️ p5.js Web Editor Sketch: https://editor.p5js.org/codingtrain/sketches/G6qbMmaI 🎥 Previous video: https://youtu.be/6z7GQewK-Ks?list=PLRqwX-V7Uu6ZiZxt
From playlist Coding Challenges
How do you make a Julia set: an escape time algorithm in python
An introduction to "what are Julia sets" and escape time algorithms by answering the question, "how do you make a Julia set". After going through the mathematical definition of a Julia set, I talk through an escape time algorithm in python that can be used to generate a Julia set. The meth
From playlist The New CHALKboard
Continues from here: http://youtu.be/NGMRB4O922I Featuring Dr Holly Krieger from MIT. Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Google Plus: http://bit.ly/numberGplus Tumblr: http:/
From playlist Mandelbrot Set - Numberphile
R. Dujardin - Some problems of arithmetic origin in complex dynamics and geometry (part1)
Some themes inspired from number theory have been playing an important role in holomorphic and algebraic dynamics (iteration of rational mappings) in the past ten years. In these lectures I would like to present a few recent results in this direction. This should include: the dynamica
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Coding Fractals in HTML with JavaScript
The first 1,000 people to use the link or my code tomrocksmaths will get a 1 month free trial of Skillshare: https://skl.sh/tomrocksmaths04221 University of Oxford Mathematician Dr Tom Crawford learns how to create beautiful mathematical art based on the Julia Fractal using HTML. Try t
From playlist Coding
Kirill Lazebnik: Transcendental Julia sets of minimal Hausdorff dimension
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 21, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Analysis and its Applications
The journey to Julia 1.0: The "Ju" in Jupyter
The journey to Julia 1.0: The "Ju" in Jupyter Viral Shah (Julia Computing), Jane Herriman (Julia Computing), Stefan Karpinski (Julia Computing, Inc.) Julia has seen over 2M downloads since its inception and v1.0 is expected to be released soon. It is used in areas as diverse as machine le
From playlist JupyterCon in New York 2018
DSI | Julia, The Power of Language by Alan Edelman
Abstract: The Julia language has become well known for its combination of performance and ease-of-use. We argue the real power of language is the ability to have impact. In this talk we will assume no or little familiarity with the Julia language, and describe why Julia is not just anoth
From playlist DSI Virtual Seminar Series
DSI | Julia, The Power of Language by Alan Edelman
Abstract: The Julia language has become well known for its combination of performance and ease-of-use. We argue the real power of language is the ability to have impact. In this talk we will assume no or little familiarity with the Julia language, and describe why Julia is not just anoth
From playlist DSI Virtual Seminar Series
Holly Krieger, Equidistribution and unlikely intersections in arithmetic dynamics
VaNTAGe seminar on May 26, 2020. License: CC-BY-NC-SA. Closed captions provided by Marley Young.
From playlist Arithmetic dynamics
In this short video I show you just how easy it is to create environments in Julia. It is very important to keep separate environments for your projects. Environments allow you to keep versions of individual packages separate from your base Julia installations. I will go as far as stati
From playlist Julia on Coursera