# Manipulate of Region Plot

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?

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}]

• I get the following: Tag Function in ({Log[t,Abs[Indexed[#1,1]]],Log[t,Abs[Indexed[#1,2]]]}&)[t_] is Protected. – user44636 Jun 9 '15 at 16:05
• 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. – andy269 Jun 9 '15 at 16:17
• Dear Andreas! Thank you for you help but I get something strange result: "{ParametricRegion[{{Log[Abs[x]]/Log,Log[Abs[y]]/Log},1+x+y=\ =0},{x,y}]} is not a valid region to plot." – user44636 Jun 9 '15 at 16:26
• 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,Log[Abs[y]]/Log},1+x+y==0},{x,y}]} is not a valid region to plot" – user44636 Jun 9 '15 at 16:33
• 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? – andy269 Jun 9 '15 at 16:36