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I try to illustrate a generation of an amoeba to a tropical curve, namely.

r0 = ComplexExpand[region["Line"] = ImplicitRegion[x + y + 1 == 0, {x, y}], {x, y}];
f = {Log[t, Abs[Indexed[#, 1]]], Log[t, Abs[Indexed[#, 2]]]} &;
r1 = TransformedRegion[r0, f];
Manipulate[ ParametricRegion[r1, t], {t, 100, 1000, 10}]    

Unfortunately, I don't get the result. How I can improve my code to get the illustration?

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You could try this:

region["Line"] = ImplicitRegion[x + y + 1 == 0, {x, y}];
r0 = ComplexExpand[region["Line"], {x, y}];
f[t_] := {Log[t, Abs[Indexed[#, 1]]], Log[t, Abs[Indexed[#, 2]]]} &;
r1[t_] := TransformedRegion[r0, f[t]];
Manipulate[RegionPlot[r1[t]], {t, 100, 1000, 10}]
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  • $\begingroup$ I get the following: Tag Function in ({Log[t,Abs[Indexed[#1,1]]],Log[t,Abs[Indexed[#1,2]]]}&)[t_] is Protected. $\endgroup$ – user44636 Jun 9 '15 at 16:05
  • $\begingroup$ Could it be that you have multiple definitions of the same object causing this issue? You could try to clear the global context using Clear["Global*"]` and re-run the code above. Alternatively you could try to restart Mathematica. $\endgroup$ – andy269 Jun 9 '15 at 16:17
  • $\begingroup$ Dear Andreas! Thank you for you help but I get something strange result: "{ParametricRegion[{{Log[Abs[x]]/Log[100],Log[Abs[y]]/Log[100]},1+x+y=\ =0},{x,y}][100]} is not a valid region to plot." $\endgroup$ – user44636 Jun 9 '15 at 16:26
  • $\begingroup$ I've just copy-paste your code and don't get any picture, I only get following: "AspectRatio->1 is not a valid variable." "ParametricRegion called with 1 argument; 2 arguments are expected. " "ParametricRegion is not a Graphics primitive or directive" " {ParametricRegion[{{Log[Abs[x]]/Log[100],Log[Abs[y]]/Log[100]},1+x+y==0},{x,y}][100]} is not a valid region to plot" $\endgroup$ – user44636 Jun 9 '15 at 16:33
  • $\begingroup$ The code I posted above works fine in Mathematica 10.1. I did not fix the aspect ratio, I only made minimal changes. So, if you start Mathematica, open a new notebook and copy-paste the code above it does not produce the plots? $\endgroup$ – andy269 Jun 9 '15 at 16:36

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