Questions tagged [recursion]
For questions about defining recursive functions, recursive algorithms and solving recursive equations.
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How can I use Mathematica's graph functions to cheat at Boggle?
Boggle is a word game played with 16 dice and a 4x4 tray. This question is inspired by a Stack Overflow question about Boggle that I decided to solve using Mathematica. In addition to Mathematica, I ...
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How can I implement dynamic programming for a function with more than one argument?
Dynamic programming is a technique for avoiding the repeated computation of the same values in a recursive program. Each value computed is immediately stored. If the value is needed again, it is not ...
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Smooth Peter de Jong attractor
Today I was playing with Peter de Jong attractor.
At the bottom of the page I've linked there are beautiful examples like:
My attempts are not so great:
It is around 10^5 points. For more than 5*10^...
Kuba♦
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How to clear parts of a memoized function?
I have a function of two variables, e.g.:
f[a_, b_] := f[a, b] = something f[a - 1, b - 1] etc
With the above code I used the concept of memoization to speed up ...
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What tools can help in realizing tail recursion?
I had nice discussions with Leonid and Rojo that got me interested in tail recursion. Tail recursion is not always easy to realize with Mathematica, so it would be nice to have some tools to help with ...
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Alternative ways to implement a triangular recursion
Triangular recursions are a class of algorithms that frequently turn up in computational mathematics. These recursions are expressible in the general form
$$T_k^{(n)}=f(T_{k-1}^{(n)},T_{k-1}^{(n+1)})$...
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Visualisation of a recursive function
Is there a way to nicely visualize recursive functions? (diagrams/plots)
More specifically I'm looking for a way to make contrast (visually) between e.g. the cosine function which if continuously ...
- 504
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How to define a recursive pattern?
I want to translate this recursive syntactic definition into a Mathematica pattern1:
$$
\mathtt{x}:
\begin{cases}
\text{Null}\\
\{\textit{integer}, \mathtt{x}\}
\end{cases}
$$
In other ...
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How can I evaluate only a single step of a recursive function?
Let's say have a simple recursive function for the Fibonacci sequence
f[0] := 1
f[1] := 1
f[n_] := f[n - 1] + f[n - 2]
but I want to see how it will expand in a ...
- 397
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Recursively appending elements to a list
In wanting to demonstrate the power of Mathematica, I wanted to show my 11-year-old son how we could validate that his sequences homework was correct. We could generate the next value in sequence in a ...
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How to implement recursive function
I'm trying to do the following (taken from an answer by Watson to my question on Math SE):
Start with $x_1=2$, say. Then define $$x_{n+1} = |\{i \in \{1,\dots,n-1\} \;:\; x_i=x_n\}|$$ i.e. number ...
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How to create a spiral using Golden Triangles
Working with students in a pre-calculus class, an application of the sine law.
They are working on a question that has them create a Golden Triangle (A golden triangle is an isosceles triangle in ...
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Efficient backtracking with Mathematica
Backtracking is a general algorithm for finding all (or some) solutions to some computational problem, that incrementally builds candidates to the solutions, and abandons each partial candidate c ("...
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How can I define a Listable function only apply to a vector?
Consider the function f which should behave as
f[{{1, 2}, {3, 4}, {5, 6, 7}}]
...
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