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Iterations

Calculate
algebraic series
such as e = 1+ 1/2! + 1/3! + ..., a square wave,Fibonacci numbers.
Study iterative maps, e.g. the (one-dimensional)
Logistic map:
(see below) or more complicated multi-dimensional maps. The logistic map is perhaps one of the simples mathematical system showing many characteristics
of the development of
chaotic
behaviour. Several analytical tools
are valailable to study the results of Iterations and ODE's such as:

A special window has been added in Mathgrapher v2 to allow detailed presentation
of 2D orbits at the pixel level and to study the stability of the orbits (see the Examples and Demonstrations for the Henon map, Standard map and Mandelbrot and Julia sets.

Iterations: Examples - series representation square wave

Series representation of square wave

Define F1=F2 and F2=F1+sin((2n+1)*x)/(2*n-1) with initial values 0.
Vary one parameter in the Iteration type panel.
Vary x and do 50 iterations (N=50) for 200 values of x ranging from -5 to 15.
This yields the following graph (this is also shown in one of the demonstrations)

The function was calculated for 200 x-values (N=50).