My Math Forum  

Go Back   My Math Forum > Math Forums > Math

Math General Math Forum - For general math related discussion and news


Thanks Tree2Thanks
  • 2 Post By romsek
Reply
 
LinkBack Thread Tools Display Modes
August 26th, 2019, 12:39 AM   #1
Senior Member
 
Joined: May 2015
From: Arlington, VA

Posts: 472
Thanks: 29

Math Focus: Number theory
Chaotic, nonlinear, fractal

How do the properties chaotic, nonlinear and fractal interrelate?
Loren is offline  
 
August 26th, 2019, 10:06 AM   #2
Senior Member
 
romsek's Avatar
 
Joined: Sep 2015
From: USA

Posts: 2,648
Thanks: 1476

Nonlinear differential equations can have solutions such that a tiny change in initial conditions results in an enormous change in the solution trajectory. These solutions are known as chaotic as while they are entirely deterministic given the exact initial conditions, in practice this is never satisfied and the trajectories may as well be random.

The boundary of sets of initial conditions that result in similar trajectories, at least in that they converge to the same attractor, can exhibit fractal geometry.

That's the 30 second version. There are far more detailed and higher quality answers available on the web.
Thanks from Loren and NinjaX3
romsek is offline  
Reply

  My Math Forum > Math Forums > Math

Tags
chaotic, fractal, nonlinear



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Fractal Programming boy129349 Art 1 February 22nd, 2012 08:21 AM
Fractal Program boy129349 Computer Science 3 February 6th, 2012 07:13 AM
Fractal Spirograph (Fractal Roulette) benice Art 3 February 1st, 2012 12:22 PM
Chaotic behavior of dynamic systems dantekavala Applied Math 0 January 13th, 2012 06:08 AM
Fractal Binary ashesmi Number Theory 0 December 31st, 1969 04:00 PM





Copyright © 2019 My Math Forum. All rights reserved.