Open source cross-platform software of geometry, analysis and simulation - Yves Biton
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Complex recurrent sequences with MathGraph32

publication Monday 31 January 2011.

MathGraph32 allows the user to create and graph recurrent sequences kind of $u_{n+1}=f(u_n)$.


Create a new figure with menu item File - New Figure with - Frame with vectors. Choose an orthonormal frame and name vectors u and v.

Via icon create a free point and get it named M with tool .

Use menu Calculus - Measure>> Point affix or click on icon to measure the affix of point M just click on M).

With menu item Calculus - New complex calculus >> Complex function (keyborad shortcut Ctrl + Maj + E) create a complexe function of a variable named f with formula f(t)=t+1/t^2.

Let’s now create a recurrent complex sequence. The starting term will be the affix previously measured.

For this, use menu item Calculs - New complex calculus - Complex u(n+1)=f[u(n)] sequence .

A dialog box pops up.
Enter u in the field Name.

Function f is already selected.

Use button Values to choose Aff(M,O,I,J) which represents the affix of point M in the text field First term.

In the field Number of terms enter 100.

Validate by OK.

Let’s now create the graph oh this sequence.

Activate on the right side of the window the blue color and the dotted line style.

Then use menu item Create - u(n+1)=f[u(n)] sequence graph - Complex.

A dialog box is opening.

Sequence u is already selected. Validate.
The figure is now ready.

On the figure underneath animated via MathGraph32 Javacript library you can capture and move point M.