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Generate random points in a unit circle using a "For" loop?

Posted 4 months ago
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I am new to Mathematica and I have a problem with the "For" statement. I am often in doubt where to place a "," or a ";".

I am stuck with the following : I want to generate random points in a unit circle with the following function :

randompunten[n_] := Module[{p = n, r, angle, lis, i},
  lis = {};
  For[i = 0;
   r = RandomReal[],
   angle = RandomReal[2 \[Pi]],
   i <= p;
   i++;

lis = Append[lis, Point[{r Cos[angle], r Sin[angle]]}]]]; lis]

The result is an empty lis

NB : I just found out that this is not the right way but aside of that : what am I doing wrong in the code ? (When I do the Append statement outside the module things work fine .

6 Replies

The , (not the ;) separates arguments, and For needs to have precisely 4 arguments.

If you are a beginner, I suggest you simply forget that For even exists, and use other constructs instead. For is never necessary, and it is very, very rarely the best option. See here for more details:

https://mathematica.stackexchange.com/questions/134609/why-should-i-avoid-the-for-loop-in-mathematica

This post discusses precisely the type of problem you are trying to solve, so be sure to read through all of it. You can do the same with a shorter and faster Table.

Posted 4 months ago

Thank you for your reply. I tried with the Do command and indeed no problem there.

Chiel Geeraert

randompunten[n_] := Module[{p = n, r, angle, lis, i}, lis = {};
  For[i = 0, i < p, 
   i++, {r = RandomReal[], angle = RandomReal[2 \[Pi]],
    lis = Append[lis, Point[{r Cos[angle], r Sin[angle]}]]}]; lis]
{Graphics[{Red, randompunten[5], Blue, Circle[{0, 0}, 1]}], 
 Graphics[{Red, randompunten[100], Blue, Circle[{0, 0}, 1]}]}

fig 1

Posted 4 months ago

This really clears thing up for me. Thank you (and mr Horvat) very much for your comments.

Chiel Geeraert

Just for completeness: The function RandomPoint should at least be mentioned.

Posted 4 months ago

Even more simple ! Alas, function not available in my version.

Thank you for your reply, Chiel Geeraert.

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