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Obtain numerical values with NestList on a custom function f?

Dag Now, home
Posted 6 years ago
POSTED BY: Dag Now
7 Replies
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Dag Now
Dag Now, home
Posted 6 years ago

Sorry, the above starts at 1 (not 0)
POSTED BY: Dag Now
Dag Now
Dag Now, home
Posted 6 years ago

And yet another way to do it: with c=-1, and starting at 0:

RecurrenceTable[{z[n + 1] == (z[n])^2  - 1, z[1] == 1}, z, {n, 1, 5}]

which gives

{0, -1, 0, -1, 0}
POSTED BY: Dag Now
Dag Now
Dag Now, home
Posted 6 years ago

Actually, I was wrong. Here is the correct way to get the iteration (still based on your answer):

f[{z_, c_}] := {z^2 + c, c}

and then

NestList[f, {0, -1}, 5]

which gives

{{0, -1}, {-1, -1}, {0, -1}, {-1, -1}, {0, -1}, {-1, -1}}

where the first argument is the iterated value of the function, and the second argument is just the constant c
POSTED BY: Dag Now
Updating Name
Updating Name
Posted 6 years ago

Another way to do it

ClearAll[f]
f[c_][z_] := z^2 + c

(* c = -1, start with 0 *)
NestList[f[-1], 0, 5]
(* {0, -1, 0, -1, 0, -1} *)    

(* c = -1, start with 3 + I *)
NestList[f[-1], 3 + I, 5]
(* {3 + I, 7 + 6 I, 12 + 84 I, -6913 + 2016 I, 43725312 - 27873216 I, 1134986739314687 - 2437530132086784 I} *)
POSTED BY: Updating Name
Dag Now
Dag Now, home
Posted 6 years ago

I followed your suggestion and I now write my function as follows:

f[{z_, c_}] := z^2 + c;

this yields 7 + 6 I for f[{3 + I, -1}] and 

In[64]:= NestList[f, {3 + I, -1}, 5]

Out[64]= {{3 + I, -1}, 7 + 6 I, 13 + 84 I, -6887 + 2184 I,   42660913 - 30082416 I, 915001745596513 - 2566686663611616 I}

So it looks like it is able to iterate now. Thanks!

By the way, why does the { } solves the problem?
POSTED BY: Dag Now
Bill Nelson
Bill Nelson
Posted 6 years ago

Can you adapt something like this?

f[{z_,c_}]:={z^2,z-c};
f[{3+I,-1}]
NestList[f,{3+I,-1},5]

which accepts a list of two items and returns a list of two items.
POSTED BY: Bill Nelson
Dag Now
Dag Now, home
Posted 6 years ago

Found the problem f is a function of two variables.

So the question now is: how can I iterate over a function of two variables?
POSTED BY: Dag Now
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