File:Exponential Function (Abs Imag Part at Infinity) Density.png
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DescriptionExponential 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: |
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Date | ||||
Source | Own drawing, Plotted in MuPAD, code given below. | |||
Author | Inductiveload | |||
Permission (Reusing this file) |
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Other versions | See Exponential function for related graphics. |
MuPAD Code[edit]
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
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 18:25, 25 April 2007 | 850 × 700 (130 KB) | Inductiveload (talk | contribs) | {{Information |Description=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} \r | |
18:19, 25 April 2007 | 850 × 700 (130 KB) | Inductiveload (talk | contribs) | Reverted to earlier revision | ||
18:11, 25 April 2007 | 850 × 700 (130 KB) | Inductiveload (talk | contribs) | Reverted to earlier revision | ||
18:09, 25 April 2007 | 850 × 700 (130 KB) | Inductiveload (talk | contribs) | New smoother colour scheme | ||
18:08, 25 April 2007 | 850 × 700 (130 KB) | Inductiveload (talk | contribs) | New smoother colour scheme. | ||
02:06, 22 April 2007 | 850 × 700 (139 KB) | Inductiveload (talk | contribs) | {{Information |Description=Diagram of the absolute value real part of exponetial 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) |
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