Contour plot: Difference between revisions

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==Implementation of contour plot in high level languages==
==Implementation of contour plot in high level languages==
[[Image:FixedPointsLoge00.png|300px|thumb|Fig.2. Contour plot of function <math>f=|z-\ln(z)|</math> in the complex
[[Image:FixedPointsLoge00.png|200px|thumb|Fig.2. Contour plot of function <math>f=|z-\ln(z)|</math> in the complex
<math>z</math>-plane, made with [[Mathematica]].]]
<math>z</math>-plane, made with [[Mathematica]].]]
[[Programming language]]s of high level ([[Matlab]], [[Mathematica]], [[Maple]]) offer the special [[procedure]]s (operators, "functions") for ''contour plot'' and ''implicit plot''. These procedures allow quick programming of contour plots of simple functions (see, for ex., Fig.2 and its source), but may be slow in execution and sometimes do not provide a good compromise between quality of the image and size of the file. Customised codes (like that used to plot Figure 1) may be more efficient, but require some effort for programming.
[[Programming language]]s of high level ([[Matlab]], [[Mathematica]], [[Maple]]) offer the special [[procedure]]s (operators, "functions") for ''contour plot'' and ''implicit plot''. These procedures allow quick programming of contour plots of simple functions (see, for ex., Fig.2 and its source), but may be slow in execution and sometimes do not provide a good compromise between quality of the image and size of the file. Customised codes (see examples below) may be more efficient, but require some effort for programming.


==Use of Contour plot==
The following figures were generated using the contour plot:
[[Image:Logez02.jpg|70px]]
[[Image:TaylorExampleZ.jpg|140px]]
<!-- Factorial !-->
[[Image:LogFactorialZ.jpg‎|100px]]
[[Image:Factorialz.jpg|100px]]
[[Image:OneOverFactorial.jpg|100px]]
<!-- tetration !-->
[[Image:Sqrt(exp)(z).jpg|120px]][[Image:ZpluxSinZ.jpg|100px]]
[[Image:TetrationModified.jpg|140px]]
[[Image:TetrationModifiedZoom.jpg|120px]]
[[Image:AnalyticTetrationBaseSqrt2u00.png|80px]]
[[Image:AnalyticTetrationBaseEv00.gif|140px]]
[[Image:Analytic4thAckermannFunction00.jpg|160px]]
[[Image:SlogFitFixedPoint04.jpg|70px]]
[[Image:SLOGtailor16.jpg|70px]]
[[Image:SLOGappro50.jpg|70px]]
[[Image:SLOGtest50.jpg|200px]]
==External examples==
More examples of contour plots and speculations around can be found at Wikipedia http://en.wikipedia.org/wiki/Contour_plot
More examples of contour plots and speculations around can be found at Wikipedia http://en.wikipedia.org/wiki/Contour_plot

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Fig.1. Function is plotted in the range , . Levels are shown wiht red lines. Levels are shown wiht blue lines.

Contour plot is kind of graphical image that shows some function with lines

(1) ,

where is constant, called level. Such lines are called isolines. If many isolines are shown, their density indicate the slop of the function.

One example of the contour plot is shown in Figure 1. Function is plotted in the range , . Levels are shown wiht red lines. Levels are shown wiht blue lines.

An isoline actually is graphic of solution of equation (1). One of variables (for example, ) can be considered as independent variable, then, another variable can be treated as solution. Graphic of one isoline is called implicit plot. Contour plot can be considered as set of implicit plots, corresponding some sequence of levels.

Countour plots are used to map some surface: relief of the Earth surface at a geographic map, real and imaginary part of a function of complex variable - any bidimensional distribution.

Implementation of contour plot in high level languages

Fig.2. Contour plot of function in the complex -plane, made with Mathematica.

Programming languages of high level (Matlab, Mathematica, Maple) offer the special procedures (operators, "functions") for contour plot and implicit plot. These procedures allow quick programming of contour plots of simple functions (see, for ex., Fig.2 and its source), but may be slow in execution and sometimes do not provide a good compromise between quality of the image and size of the file. Customised codes (see examples below) may be more efficient, but require some effort for programming.

Use of Contour plot

The following figures were generated using the contour plot:

Logez02.jpg TaylorExampleZ.jpg LogFactorialZ.jpg Factorialz.jpg OneOverFactorial.jpg Sqrt(exp)(z).jpgZpluxSinZ.jpg TetrationModified.jpg TetrationModifiedZoom.jpg AnalyticTetrationBaseSqrt2u00.png AnalyticTetrationBaseEv00.gif Analytic4thAckermannFunction00.jpg SlogFitFixedPoint04.jpg SLOGtailor16.jpg SLOGappro50.jpg SLOGtest50.jpg


External examples

More examples of contour plots and speculations around can be found at Wikipedia http://en.wikipedia.org/wiki/Contour_plot