Premium Only Content
DépêcheMath - Mandelbrot sequence f₀(z) = 0; fₙ₊₁(z) = (fₙ(z))² + z
Animated development of the "Mandelbrot" sequence f₀(z) = 0; fₙ₊₁(z) = (fₙ(z))² + z with some mathematical annotations and explanations.
Music: Doug Maxwell, Cast of Pods
This animation covers the recursively defined sequence of polynomials f₀(z) = 0; fₙ₊₁(z) = (fₙ(z))² + z which is closely related to the famous Mandelbrot fractal set. Its development is depicted by coloring the points of the complex plane according to the values of fₙ(z). See the legend in the lower left corner for how to translate these colors to complex values or halt this animation at f₁(z) = z which is the identity map and study the correspondence between colors and positions in the complex plane.
Speaking in terms of dynamical systems theory, we discuss this recursion not in the dynamic plane but rather in the parameter plane and study the sequence members as functions of this parameter.
Animation imaging was created using "Complex Plane Viewer" (CPV), a program written by myself for visualizing complex functions, developed within the Lazarus IDE.
Watch this video in Full HD resolution (1080p) and full screen mode for best viewing experience.
-
2:12
Math lessons
3 years agoFINITE OR INFINITE SEQUENCE
16 -
16:28
JTMYOGALLC
3 years agoEasy Hip Opener Sequence
154 -
4:13
perilousjames
3 years agosequence stuff
9 -
1:26:31
Josh Pate's College Football Show
5 hours ago $1.59 earnedSEC Disaster Saturday | Major CFP Earthquake Coming | Officiating Is A Disaster | New Studio Debut
16.1K -
1:43:05
Adam Does Movies
9 hours ago $0.29 earnedGladiator II Spoiler Conversation With Hack The Movies
19.8K -
24:10
Bwian
9 hours agoI Don't Know What I'm Doing in Fortnite, But I Still Won...
15.6K1 -
19:30
DeVory Darkins
11 hours ago $3.32 earnedJoe Rogan MOCKS The View as Bill Maher HUMILIATES Woke Scientist
90.4K122 -
11:25:41
Scottish Viking Gaming
12 hours agoSUNDAY FUNDAY | Jump into my Sons of the Forest Game | DOO EET NOWWA!
90.2K1 -
24:01
Winston Marshall
4 days agoThe TRUTH About The UK Farmer Protest What No One Is Talking About...
82.8K174 -
3:21:56
Tate Speech by Andrew Tate
17 hours agoEMERGENCY MEETING EPISODE 93 - ME TOO!
291K195