FixedPointsLoge00/code

(* source in Mathematica that generates the contour plots *)
(*  and   *)
(* that isustrate graphical search of fixed points of logarithm and those of exponential *)
(* Copyleft 2008 by Dmitrii Kouznetsov *)

<< Graphics`ImplicitPlot`
RGB[r_,g_,b_]=RGBColor[r,g,b];

f = Abs[x + I*y - Log[x + I*y]];
iplo = ImplicitPlot[{f == .5, f == 1, f == 2, f ==4,f ==8, f ==16,f==32}, {x,-10,10.1}, {y,-2,21},
     PlotStyle -> {RGB[0,0,0],RGB[0,0,0],RGB[.5,0,0],RGB[1,0,0],RGB[0,1,0],RGB[0,0,1],RGB[1,0,1]}, 
     AspectRatio -> Automatic, PlotPoints -> 200, PlotRange -> {{-10, 10.1}, {-2, 21}}];

Export["iplo.eps",iplo]
Export["iplo.pdf",iplo]
Export["iplo.png",iplo]
Export["iplo.svg",iplo]
Export["iplo.jpg",iplo]

f = Abs[x + I*y - Exp[x + I*y]]; 
ipex = ImplicitPlot[{f==.5, f==1,f ==2,f == , f == 8, f == 16, f == 32}, {x, -9, 4.2}, {y,-2,21}, 
PlotStyle -> {RGB[0,0,0],RGB[0,0,0],RGB[.5,0,0],RGB[1,0,0],RGB[0,1,0],RGB[0,0,1],RGB[1,0,1]}, 
AspectRatio -> Automatic,PlotPoints -> 200];

Export["ilex.eps",ipex]
Export["ilex.pdf",ipex]
Export["ilex.png",ipex]
Export["ilex.svg",ipex]
Export["ilex.jpg",ipex]

M = 2.062277729598284 + 7.5886311784725127I; 
f =  100000000000000 Abs[M + x + I*y - Exp[M + x + I*y]]; ImplicitPlot[{f==1,f==2,f==6,f==20}, 
{x, -.00000000000001, .00000000000001}, {y, -.00000000000001, .00000000000001}, 
PlotStyle -> {RGB[1,0,0],RGB[0,.5,0], RGB[0,0,1], RGB[1,0,1]}, PlotPoints -> 90, PlotRange -> All];

(* Copyleft 2008 by Dmitrii Kouznetsov *)