Portal:Mathematics
Template:/Random portal component
Lua error in package.lua at line 80: module 'Module:Box-header/colours' not found.
 |
The Lorenz attractor is an iconic example of a strange attractor in chaos theory. This three-dimensional fractal structure, resembling a butterfly or figure eight, reflects the long-term behavior of a set of solutions to the Lorenz system, three differential equations used by mathematician and meteorologist Edward N. Lorenz as a simple description of fluid circulation in a shallow layer heated uniformly from below and cooled uniformly from above. Analysis of the system revealed that although the solutions are completely deterministic, they develop in complex, non-repeating patterns that are highly dependent on the exact values of the parameters and initial conditions. As stated by Lorenz in his 1963 paper Deterministic Nonperiodic Flow, "Two states differing by imperceptible amounts may eventually evolve into two considerably different states". He later coined the term "butterfly effect" to describe the phenomenon. The particular solution plotted in this animation is based on the parameter values used by Lorenz (σ = 10, ρ = 28, and β = 8/3). Initially developed to describe atmospheric convection, the Lorenz equations also arise in simplified models for lasers, electrical generators and motors, and chemical reactions.
Template:/box-header Template:/Did you know Template:/box-footer-empty
Template:/box-header Template:/Projects Template:/box-footer-empty
Template:/box-header Template:/Things you can do Template:/box-footer-empty
Template:/box-header Template:/Categories Template:/box-footer
Template:/box-header Template:/Index Template:/box-footer-empty
Template:/box-header Template:/RelatedPortals Template:/box-footer-empty
Template:/box-header Template:/OtherWikimedia Template:/box-footer-empty
