Premium Only Content

DépêcheMath - Mandelbrot sequence f₀(z) = 0; fₙ₊₁(z) = (fₙ(z))² + z without subtitles
Animated development of the "Mandelbrot" sequence f₀(z) = 0; fₙ₊₁(z) = (fₙ(z))² + z without mathematical subtitles.
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.
-
LIVE
The Quartering
2 hours agoDangerous ICE Tracker App, Luigi Mangione Bombshell, H1-B's Blown Out, EBT Meltdowns!
8,206 watching -
DeVory Darkins
15 hours ago $28.95 earnedDemocrats drop SHOCKING Update regarding ICE Agents - Myron Gaines
104K45 -
LIVE
Mally_Mouse
1 hour ago📣Telescreen Talks - LIVE!
112 watching -
21:24
Professor Nez
57 minutes ago🚨WOW! Trump got EMOTIONAL when RFK Jr. Said THIS!
1198 -
LIVE
Jeff Ahern
38 minutes agoNever woke Wednesday with Jeff Ahern
61 watching -
1:06:21
Timcast
3 hours agoLiberals DEFEND Nazi Tattoo On Communist Democrat Senate Candidate, ITS A CULT
120K121 -
LIVE
Side Scrollers Podcast
2 days ago🔴FIRST EVER RUMBLE SUB-A-THON🔴DAY 3🔴100% REVENUE HELPS CHANGE CULTURE!
1,304 watching -
25:57
The Kevin Trudeau Show Limitless
5 hours agoThe Sound Of Control: This Is How They Program You
3.4K4 -
LIVE
Dr Disrespect
3 hours ago🔴LIVE - DR DISRESPECT - BATTLEFIELD 6 KILL CHALLENGE - VS VISS
1,264 watching -
11:32
Sponsored By Jesus Podcast
3 days agoWhat “Speaking the Truth in Love” REALLY Means | Tension of Grace and Truth
10.6K5