0
$\begingroup$

I'm new tho mathematica.

I have a complex sequence ${z_n}$ with

$z_0:=c$

$z_{n+1}=(z_n)^2+c$ for all $n\in N$

where c is some complex number, I need to plot the first 20 terms of this sequence where $c=-0.5+0.2i$, print the plot and for the value of $c$ in $(a)$ determin it's limit.

The main problem is that i don't know from where to start...

$\endgroup$

1 Answer 1

2
$\begingroup$

For basic function construction see: http://reference.wolfram.com/language/tutorial/MakingDefinitionsForFunctions.html

You did not explain how you want to plot a complex valued function but here's a start:

c = -0.5 + 0.2 I;
z[0] := c
z[n_Integer?Positive] := z[n - 1]^2 + c

Array[z, 20]
{-0.29 + 0. I, -0.4159 + 0.2 I, -0.367027 + 0.03364 I, -0.366423 + 
  0.175306 I, -0.396467 + 0.0715275 I, -0.34793 + 0.143283 I, -0.399475 + 
  0.100295 I, -0.350479 + 0.11987 I, -0.391533 + 0.115976 I, -0.360152 + 
  0.109183 I, -0.382211 + 0.121355 I, -0.368642 + 0.107233 I, -0.375602 + 
  0.120939 I, -0.373549 + 0.10915 I, -0.372375 + 0.118454 I, -0.375368 + 
  0.111781 I, -0.371594 + 0.116082 I, -0.375393 + 0.11373 I, -0.372015 + 
  0.114613 I, -0.374741 + 0.114724 I}

For plotting complex values perhaps start here: Plotting complex Sine

$\endgroup$
1
  • 1
    $\begingroup$ The now built-in functions for plotting Julia and Mandelbrot sets might also be of interest to the OP. $\endgroup$ Commented May 12, 2015 at 23:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.