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matplotlib.org. Matplotlib (portmanteau of MATLAB, plot, and library [3]) is a plotting library for the Python programming language and its numerical mathematics extension NumPy. It provides an object-oriented API for embedding plots into applications using general-purpose GUI toolkits like Tkinter, wxPython, Qt, or GTK.
Lorenz 96 model. The Lorenz 96 model is a dynamical system formulated by Edward Lorenz in 1996. [1] It is defined as follows. For : where it is assumed that and and . Here is the state of the system and is a forcing constant. is a common value known to cause chaotic behavior. It is commonly used as a model problem in data assimilation.
Logistic map. The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often referred to as an archetypal example of how complex, chaotic behaviour can arise from very simple nonlinear dynamical equations.
File:Sierpinski triangle.svg. Size of this PNG preview of this SVG file: 692 × 599 pixels. Other resolutions: 277 × 240 pixels | 554 × 480 pixels | 887 × 768 pixels | 1,182 × 1,024 pixels | 2,364 × 2,048 pixels | 1,024 × 887 pixels. Original file (SVG file, nominally 1,024 × 887 pixels, file size: 3 KB) This is a file from the ...
from matplotlib.pyplot import * from numpy import linspace from scipy.stats import beta x = linspace (0, 1, 75) fig = figure ax = fig. add_subplot (111) ax. plot (x ...
An animated cobweb diagram of the logistic map y = r x (1-x), showing chaotic behaviour for most values of r > 3.57. A cobweb plot, known also as Lémeray Diagram or Verhulst diagram is a visual tool used in the dynamical systems field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions, such as the ...
Subplot. In fiction, a subplot or side story is a strand of the plot that is a supporting side story for any story or for the main plot. Subplots may connect to main plots, in either time and place or thematic significance. Subplots often involve supporting characters, those besides the protagonist or antagonist.
Lorenz system. A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8 3 . The Lorenz system is a system of ordinary differential equations first studied by mathematician and meteorologist Edward Lorenz. It is notable for having chaotic solutions for certain parameter values and initial conditions.