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The [[wp:Padovan sequence|Padovan sequence]] is similar to the [[wp:Fibonacci sequence|Fibonacci sequence]] in several ways.
Some are given in the table below, and the referenced video shows some of the geometric
similarities.
::{| class="wikitable"
! Comment !! Padovan !! Fibonacci
|-
| || ||
|-
| Named after. || Richard Padovan || Leonardo of Pisa: Fibonacci
|-
| || ||
|-
| Recurrence initial values. || P(0)=P(1)=P(2)=1 || F(0)=0, F(1)=1
|-
| Recurrence relation. || P(n)=P(n-2)+P(n-3) || F(n)=F(n-1)+F(n-2)
|-
| || ||
|-
| First 10 terms. || 1,1,1,2,2,3,4,5,7,9 || 0,1,1,2,3,5,8,13,21,34
|-
| || ||
|-
| Ratio of successive terms... || Plastic ratio, p || Golden ratio, g
|-
| || 1.324717957244746025960908854… || 1.6180339887498948482...
|-
| Exact formula of ratios p and q. || ((9+69**.5)/18)**(1/3) + ((9-69**.5)/18)**(1/3) || (1+5**0.5)/2
|-
| Ratio is real root of polynomial. || p: x**3-x-1 || g: x**2-x-1
|-
| || ||
|-
| Spirally tiling the plane using. || Equilateral triangles || Squares
|-
| || ||
|-
| Constants for ... || s= 1.0453567932525329623 || a=5**0.5
|-
| ... Computing by truncation. || P(n)=floor(p**(n-1) / s + .5) || F(n)=floor(g**n / a + .5)
|-
| || ||
|-
| L-System Variables. || A,B,C || A,B
|-
| L-System Start/Axiom. || A || A
|-
| L-System Rules. || A->B,B->C,C->AB || A->B,B->AB
|}
;Task:
* Write a function/method/subroutine to compute successive members of the Padovan series using the recurrence relation.
* Write a function/method/subroutine to compute successive members of the Padovan series using the floor function.
* Show the first twenty terms of the sequence.
* Confirm that the recurrence and floor based functions give the same results for 64 terms,
* Write a function/method/... using the [[wp:L-system|L-system]] to generate successive strings.
* Show the first 10 strings produced from the L-system
* Confirm that the length of the first 32 strings produced is the Padovan sequence.
Show output here, on this page.
;Ref:
* [https://www.youtube.com/watch?v=PsGUEj4w9Cc The Plastic Ratio] - Numberphile video.