This article will be permanently flagged as inappropriate and made unaccessible to everyone. Are you certain this article is inappropriate? Excessive Violence Sexual Content Political / Social
Email Address:
Article Id: WHEBN0002673485 Reproduction Date:
The Tinkerbell map is a discrete-time dynamical system given by:
Some commonly used values of a, b, c, and d are
Like all chaotic maps, the Tinkerbell Map has also been shown to have periods; after a certain number of mapping iterations any given point shown in the map to the right will find itself once again at its starting location.
The origin of the name is uncertain; however, the graphical picture of the system (as shown to the right) shows a similarity to the movement of Tinker Bell over Cinderella Castle, as shown at the beginning of all films produced by Disney.
The Java source code that was used to generate the Tinkerbell Map displayed above:
import java.io.*; public class TinkerBellMap { public static void main(String[] args) throws Exception { FileWriter fstream = new FileWriter("TinkerBellMapOutput.txt"); BufferedWriter out = new BufferedWriter(fstream); int time = 0, iterations = 50000; double x = -0.72, y = -0.64; double a = 0.9, b = -0.6013, c = 2.0, d = 0.5; while (time < iterations) { double oldX = x; x = Math.pow(x,2)-Math.pow(y,2)+a*x+b*y; y = 2*oldX*y+c*oldX+d*y; out.write(x+" "+y+"\n"); //writing data to a txt file to be read by Mathematica time++; } } }
Mathematics, Physics, Meteorology, Biology, Economics
Chaos theory, Statistical mechanics, Systems science, Mathematics, Bifurcation theory
Chaos theory, Mathematics, Dynamical system, Fractals, Arnold's cat map
Adam Smith, Chaos theory, Medicine, Censorship, Social sciences
Hyperion (moon), Dynamical system, Ergodic, Mixing (mathematics), Chaotic behavior
Chaos theory, Dynamical system, Bifurcation theory, Unintended consequences, External ray
Chaos theory, Dynamical system, Duffing equation, Bifurcation theory, Unintended consequences