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| View Original: | Exponential Function (Abs Imag Part at Infinity) Density.png (850x700) | |||
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| Keywords: Exponential Function (Abs Imag Part at Infinity) Density.png Diagram of the absolute value of the real part of the exponential function in the complex plane as the operand approaches infinity The plot is given by <math>z \bigg \operatorname Im \left \exp \left \frac 1 x + i y \right \right \bigg </math> The colour code is based on the arctan function and therefore emphasises changes at small values more than changes at large values Green is smallest then blue red and yellow largest Own drawing Plotted in MuPAD code given below 2007-04-20 Inductiveload See Exponential function for related graphics MuPAD Code <pre> f abs Im exp 1/ x+I y ylimit 1 xlimit 1 mesh 1000 //resolution of density plot a 1 //change this to adjust the colour band drop-of rate fmin 0 //minimum value of colour function i e the one with arctan in it fmax 1 //maximum value of colour function range 1 //for brevity colour proc c begin if c < fmin then return 1 0 0 //this term may not be needed but it means we can deal with slightly under-limit values elif c < fmin + 1 range/6 then return 1 abs sin c-fmin PI/2 / range/6 a 0 elif c < fmin + 2 range/6 then return abs sin c-fmin PI/2 / range/6 a 1 0 elif c < fmin + 3 range/6 then return 0 1 abs -sin c-fmin PI/2 / range/6 a elif c < fmin + 4 range/6 then return 0 abs -sin c-fmin PI/2 / range/6 a 1 elif c < fmin + 5 range/6 then return abs sin c-fmin PI/2 / range/6 a 0 1 elif c < fmin + 6 range/6 then return 1 0 abs sin c-fmin PI/2 / range/6 a else return 1 0 1 end_if end_proc colfunc x y z -> colour arctan z/2 5 0001/6 / 0 5 PI //the factor of 5/6 prevents the spectrum from wrapping // by precisely one colour transition m->r //The extra 0 00001 is to prevent an error when evaluating the 5th elif clause //No idea why but it must be sometihng to do with there being a 5/6 in there cplot plot Density f x -xlimit xlimit y -ylimit ylimit AntiAliased TRUE Mesh mesh mesh AxesTitleFont Courier New Bold 14 TicksLabelFont Arial 10 FillColorFunction colfunc YTicksDistance 0 5 XTicksDistance 0 5 time plot cplot Axes Frame Width 8 5 unit inch Height 7 unit inch sec/1000 0 </pre> Complex exponential function šÂ« Image ˜<sub><tt><tt> ¹ ¹<code>··°<noinclude><tt><tt> ¹<tt>«« <sub> REDIRECT <noinclude></noinclude></sub> »»</tt> º</tt></tt></noinclude></code> º º</tt></tt></sub> ™Â» ˜ | ||||
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