Fractals | Algorithms | Complex dynamics
There are many programs and algorithms used to plot the Mandelbrot set and other fractals, some of which are described in fractal-generating software. These programs use a variety of algorithms to determine the color of individual pixels efficiently. (Wikipedia).
Stirring the Mandelbrot Set: a checkerboard
http://code.google.com/p/mandelstir/
From playlist mandelstir
The Mandelbrot set is a churning machine
Its job is to fling off the red pixels and hang onto the green ones. Audio by @Dorfmandesign
From playlist mandelstir
Mandelbrot Set Computer Rendered
Bask in the beauty of the Mandelbrot set, one of the most incredible and otherworldly constructions in mathematics. This video explores the set as generated by a computer program developed by me.
From playlist Fun
Applying the Mandelbrot mapping: inside the set is green, outside is red
Source code: https://github.com/timhutton/mandelstir The Mandelbrot z^2+c mapping is applied to every point in the radius-2 disk, with linear interpolation between iterations to show how the points move. Points that belong to the Mandelbrot set are colored in green, while those outside are
From playlist mandelstir
Applying the Mandelbrot mapping to the points outside the set
Source code: https://github.com/timhutton/mandelstir The Mandelbrot z^2+c mapping is applied to every point outside the Mandelbrot set, with linear interpolation between iterations to show how the points move. Eventually all of these points disappear as they move off to infinity. The backg
From playlist mandelstir
It's the Mandelbulb! What happens when you take the original fractal (The Mandelbrot Set) and extend it into 3D space? And how do you visualize it in Processing (Java) as a point cloud? https://thecodingtrain.com/CodingChallenges/168-mandelbulb.html 🎥 Previous video: https://youtu.be/a35K
From playlist Coding Challenges
Indra's Pearls: A Mathematical Adventure
Public Lecture by Caroline Series (University of Warwick) Here are the weblinks to the sites mentioned in the video Jos Leys Mathematical Imagery Beautiful mathematical graphics including Kleinian limit sets. http://www.josleys.com Open source software to make Kleinian limit sets. http
From playlist Public Lectures
Waves radiating from the Mandelbrot set, in 3D
This new simulation of waves interacting with the Mandelbrot set shows what happens to a circular wave starting inside the set, when the outside of the set is refracting, with an index of 2, meaning the wave speed is half as large outside the set than inside. The boundary of the Mandelbrot
From playlist Wave equation
NOTACON 6: The Uses of Disorder: Chaos Theory as it Relates to Demos
Speaker: Mark Lenigan & Kirk Lenigan Fractal graphics have been a part of the visual toolkit of the Demoscene for years now. However, they are only the tip of the iceberg when it comes the mathematics of complex, non-linear dynamical systems (popularly known as Chaos Theory). This talk wi
From playlist Notacon 6
In this video, I examine a sequence of strategies to try and improve the rendering speed of a Mandelbrot Fractal. Starting off with naive assumptions, I explore optimising the algorithm, then the use of vector co-processing, and finally threads and thread-pools in order to squeeze as much
From playlist Interesting Programming
SIMD and Vectorization: Parallelism in C++ #1/3 (multitasking on single core)
Computer programs can be made faster by making them do many things simultaneously. Let’s study three categorical ways to accomplish that in GCC. In the first episode, we explore various alternative approaches to SIMD: Single Instruction, Multiple Data. As a plot device in this tool-assist
From playlist Programming
Join Dylan Beattie - programmer, musician, and creator of the Rockstar programming language - for an entertaining look at the art of code. We’ll look at the origins of programming as an art form, from Conway’s Game of Life to the 1970s demoscene and the earliest Obfuscated C competitions.
From playlist Software Development
Applying the Mandelbrot mapping to the main cardioid
Source code: https://github.com/timhutton/mandelstir The Mandelbrot z^2+c mapping is applied to every point in the main cardioid, with linear interpolation between iterations to show how the points move. The final result seems almost evenly spread over the radius 0.5 disk centered at the o
From playlist mandelstir
The Mandelbrot Fractal Explained!
Twitter: @The_ArtOfCode Facebook: https://www.facebook.com/groups/theartofcode/ Patreon: https://www.patreon.com/TheArtOfCode The Mandelbrot fractal, or Mandelbrot set as it's sometimes called. Most people have seen its iconic shape and many of us have marveled at its beauty and complexit
From playlist Tools
Ahlfors-Bers 2014 "Roots of Polynomials and Parameter Spaces"
Sarah Koch (University of Michigan): In his last paper, "Entropy in Dimension One," W. Thurston completely characterized which algebraic integers arise as exp(entropy(f)), where f is a postcritically finite real map of a closed interval. On page 1 of this paper, there is a spectacular ima
From playlist The Ahlfors-Bers Colloquium 2014 at Yale
The dark side of the Mandelbrot set
Join the Mathologer and his guest Darth Vader as they explore the Dark Side of the Mandelbrot set. Featuring an introduction to how the Mandelbrot set and the halo surrounding it is conjured up, an ingenious way to visualise what's really going on inside the Mandelbrot set, as well as an a
From playlist Recent videos
Applying the Mandelbrot mapping to the top bulb
Source code: https://github.com/timhutton/mandelstir The Mandelbrot z^2+c mapping is applied to every point in the circle to the top of the main cardioid, with linear interpolation between iterations to show how the points move. Points in this region fall into period-3 orbits. The backgrou
From playlist mandelstir
