The default behavior is to use a rectangle which preserves the aspect ratio of the current graph. Dragging the mouse shows a rectangle which will become the new range.The last item on the toolbar indicates the current drawing mode. Dragging allows you to interactively change the position of the newly created trek.Ĭtrl +click or right-click selects treks.ĭragging the create treks button opens a menu that allows you to toggle the default drawing mode between lines and points.
Change their color using the color well toolĬtrl +click or right-click creates treks.Move their starting position (s ) by dragging.Multiple treks may be selected by dragging or using Shift + click. Even though the basic idea is simple, the idea of iteration is fundamental to most numerical methods, so a tremendous variety of methods and models can be visualized this way.
MATHEMATICA GRADIENT GENERATOR
This is a very simple generator that simply plots the result of applying NestList to a specified function. You can also see the definitions of the DifferentialEquationTrek and PoincareSection generators in the package file EquationTrekker.m. The two examples that follow have been kept simple for the purposes of illustration. The ideas behind setting up a trek generator are best illustrated by some examples. InitializeGenerator [ gname, spec, dvars, containing a new trek generator object )Īll the methods are necessary to have EquationTrekker display the modifiable items and problem specification in a reasonable way, but the essence of a particular trek generator will lie in how the "GenerateTrek" method is defined.
MATHEMATICA GRADIENT CODE
When the value of "SectionCondition" is of the form Mod, where ω and T are constants (they can depend on trek parameters, just not on the independent variable t or any of the dependent variables), a special optimized code is used to handle this common case as in the preceding example. Additionally, you can also pass to the generator any options of NDSolve you would like to be used in the computation. It is required that you specify some value for both "SectionCondition" and "SectionVariables". Method options for the PoincareSection trek generator.
An expression in the problem variables for which the section variables will be shown whenever the expression is zeroĪ subset of two of the dependent variables (or their derivatives for second- and higher-order equations ) which will be shown every time the section condition expression is zeroĪ function to apply to the values of the section variables before plotting this only affects the plot, not the selection of initial conditions
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