# Tagged Questions

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*...
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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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### 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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### 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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### Compile recursive function modifying global variables

How to compile recursive formula when it relies on more than a few global variables (global to the topmost compiled function)? It is unreasonable to pass on all such variables to each recursive ...
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### Improve speed in this tree - memoization won't suffice

I have two functions, one of which calls the other. I need to do some calculations but I was unable to optimize my code to do it efficiently. In search I came across the memoization technique, which ...
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### Compiling a recursive formula

My question is related to computing what is called "invariant measure" for a particular well known fractal - the Sierpinski triangle. We have an array m of four two by two matrices, say ...
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### Maximizing a recursive functional equation

I would like to maximize a recursive functional equation but I am struggling with setting up the problem correctly. The equation I am interested in captures the nature of a decision process over time ...
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### What do RecursionLimit and IterationLimit actually set?

The following recursive functions respectively calculate the length of a Short-cut Collatz Conjecture series and perform a pointless demonstration recursion: ...
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### Wrapping a function in count

I am working through the Programming Paradigms via Mathematica (A First Course) and am attempting to answer the following: Use recursion to count how many times the argument can have its square ...
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### Recursive partitioning: Is there a better way to do this?

Consider the following function, which recursively splits a list into equal length sublists (the length of the list is assumed to be a power of the second argument): ...
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### Second order differential equation with boundary conditions solving repeatedly

I want to solve a second order differential equation in the interval[-1:1], which does not have a analytic solution, \begin{eqnarray} y''(x) &=& k \phi^2(x)y(x) \\ \phi(x) &=& \frac{1}{...
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### Recurrences of lists

Assume we have a multi-dimensional recurrence, e.g. \qquad\begin{align*} a_1 &= (1,2) \\ a_n &= (1,2) + a_{n-1} \quad, n>1 \end{align*} with the easy solution $a_n = (n,2n)$. How ...
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### Paying off an installment

How do I determine the weekly installment I have to pay, if my loan is, let's say, loan=5000, with interest rate of 2% every ...
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### How to nest my own “times” function to get powers

I have a "times" function. I'd like to create a power function using it. It should look like this for an 6th power: ...
I am figuring out how to calculate the $n$-th step of a square root approximation sequence: $$x_{n+1} = \frac12\left(x_{n} + \frac{a}{x_n}\right),$$ where $a$ is a number the root of which is to be ...