The Mandelbrot set (/ˈmændəlbroʊt, -brɒt/) is the set of complex numbers for which the function does not diverge to infinity when iterated from , i.e., for which the sequence , , etc., remains bounded in absolute value. This set was first defined and drawn by Robert W. Brooks and Peter Matelski in 1978, as part of a study of Kleinian groups. Afterwards, in 1980, Benoit Mandelbrot obtained high quality visualizations of the set while working at IBM's Thomas J. Watson Research Center in Yorktown Heights, New York. Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications; mathematically, one would say that the boundary of the Mandelbrot set is a fractal curve. The "style" of this recursive detail depends on the region of the set boundary being examined. Mandelbrot set images may be created by sampling the complex numbers and testing, for each sample point whether the sequence goes to infinity. Treating the real and imaginary parts of as image coordinates on the complex plane, pixels may then be coloured according to how soon the sequence crosses an arbitrarily chosen threshold (the threshold has to be at least 2, as -2 is the complex number with the largest magnitude within the set, but otherwise the threshold is arbitrary). If is held constant and the initial value of is varied instead, one obtains the corresponding Julia set for the point . The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules. It is one of the best-known examples of mathematical visualization, mathematical beauty, and motif. (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
The Mandelbrot set is a complex fractal, arguably one of the most beautiful structures in mathematics. It is introduced in this video.
From playlist Fun
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
Animated Mandelbrot Transform - linear interpolation, applied to an image of the Set itself
http://code.google.com/p/mandelstir/
From playlist mandelstir
Pi and the Mandelbrot Set - Numberphile
This video features Dr Holly Krieger. More videos with Holly Krieger: http://bit.ly/HollyKrieger More links & stuff in full description below ↓↓↓ Extra footage from this interview: https://youtu.be/r8Ksuc7T-VQ Thanks to Audible --- http://www.audible.com/numberphile Since this was filme
From playlist Mandelbrot Set - Numberphile
Live Stream #43: Mandelbrot Set with p5.js
Live from sfpc.io! In this live stream, I program from scratch the Mandelbrot set using p5.js. To view the edited version of this coding challenge: https://www.youtube.com/watch?v=6z7GQewK-Ks 19:30 - Mandelbrot Set 44:50 - Back from debugging 51:35 - Experiment with coloring 1:02:24 - Co
From playlist Live Stream Archive
Coding Challenge #141: Calculating Digits of Pi with Mandelbrot Set
Happy belated Pi Day once more! Here I attempt to approximate Pi using a special location in the Mandelbrot set. The programming environment is Processing (Java). 💻 Code: https://thecodingtrain.com/CodingChallenges/141-mandelbrot-pi Links discussed in this video: 🔗 The World of Pi: http:
From playlist Coding Challenges
Coding Challenge #21: Mandelbrot Set with p5.js
In this coding challenge, I program from scratch the Mandelbrot set with p5.js Code: https://thecodingtrain.com/challenges/21-mandelbrot-set-with-p5js 🕹️ p5.js Web Editor Sketch: https://editor.p5js.org/codingtrain/sketches/KsV1wWLqd 🎥 Previous video: https://youtu.be/jrk_lOg_pVA?list=PL
From playlist Coding Challenges
mandelbrot fractal animation 5
another mandelbrot/julia fractal animation/morph.
From playlist Fractal
Holly Krieger: A case of the dynamical André-Oort conjecture
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 Dynamical Systems and Ordinary Differential Equations
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
Animated Mandelbrot transform - linear interpolation
http://code.google.com/p/mandelstir/
From playlist mandelstir