Recursion Plotting Two Recursive Functions Mathematica Stack Exchange I'm trying to plot two recursive functions (p and θ) on a map. so far i have: θ0 = pi 2; p0 = 0; α = 0.1; β = 1; θ [j ] := θ [j] = θ [j 1] β*p [j 1]; p [j ] := p [j] = p [j 1] α*sin [θ [j. While i understand the meaning of the individual functions (prepend, rest, first), i don't understand how this is a recursive function and how it actually works to give the output that it gives.
Recursion Plotting Two Recursive Functions Mathematica Stack Exchange Linear recurrences such as fibonacci are relatively easy examples. their values can be easily computed by recurrencetable or recursivefunction. this resource recursivefunction can additionally compute values of nestedly recursive functions, where recurrencetable fails with an error message. Recurrencetable [eqns, expr, {n, nmax}] generates a list of values of expr for successive n based on solving the recurrence equations eqns. recurrencetable [eqns, expr, nspec] generates a list of values of expr over the range of n values specified by nspec. Recurrences, although a very tedious computation method by hand, is very simple to do in mathematica. the best way to learn how to do recurrences in mathematica are by examples, and a perfect example for this topic is the fibonacci integer sequence. The problem is that the implicit assumption is that recursion stops when the input reaches zero. this only works when the starting input in the call of g is a positive integer, which generally won't be the case in a plot.
Recursion Plotting Two Recursive Functions Mathematica Stack Exchange Recurrences, although a very tedious computation method by hand, is very simple to do in mathematica. the best way to learn how to do recurrences in mathematica are by examples, and a perfect example for this topic is the fibonacci integer sequence. The problem is that the implicit assumption is that recursion stops when the input reaches zero. this only works when the starting input in the call of g is a positive integer, which generally won't be the case in a plot. Here is a method using recursion with memoization. the trick is to create a recursive function which returns the length of the chain to 1, rather than just the next value. so for example when starting with 10000 the next value you get is 5000 and you have already memoized that it is 29 steps from 5000 to 1, so it must be 1 29 = 30 from 10000 to 1. Let's start with simple recursive function provided by @corey979: it works as expected: but it's a bit slow: to write faster version, let's think what knowledge, about previous elements, do we need, in order to calculate next element. The slowness you're experiencing is probably due to the recursion and not due to the piecewise specifically. you can likely get around this by memoizing your recursive results:. I would like to make a plot of $x {n}$ against $n$ for the following recursive relation: $$x {n} = \frac {1} {2}\ln\left (\cosh (2x {n 1})\right)$$ i would like to plot graphs for arbitrary values of.
Recursion Plotting Two Recursive Functions Mathematica Stack Exchange Here is a method using recursion with memoization. the trick is to create a recursive function which returns the length of the chain to 1, rather than just the next value. so for example when starting with 10000 the next value you get is 5000 and you have already memoized that it is 29 steps from 5000 to 1, so it must be 1 29 = 30 from 10000 to 1. Let's start with simple recursive function provided by @corey979: it works as expected: but it's a bit slow: to write faster version, let's think what knowledge, about previous elements, do we need, in order to calculate next element. The slowness you're experiencing is probably due to the recursion and not due to the piecewise specifically. you can likely get around this by memoizing your recursive results:. I would like to make a plot of $x {n}$ against $n$ for the following recursive relation: $$x {n} = \frac {1} {2}\ln\left (\cosh (2x {n 1})\right)$$ i would like to plot graphs for arbitrary values of.
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