Data update

Task/Padovan-sequence/MATLAB/padovan-sequence.m

@@ -0,0 +1,51 @@
+clear all;close all;clc;
+% Calculate the sequences
+padovan_sequence_20 = Padovan1(20)
+padovan_approx_20 = Padovan2(20)
+
+% Check if the sequences are equal for n = 64
+are_sequences_equal = isequal(Padovan1(64), Padovan2(64))
+
+
+% Generate the substitution system sequence
+sequence_32 = createLSystem();
+words = sequence_32(1:10)
+
+% Check if the length of the substitution system sequence equals the Padovan sequence
+are_lengths_equal = all( cellfun(@(ele) length(ele), sequence_32) ...
+                                        == Padovan2(32) )
+
+function words = createLSystem()
+    words = {'A'}; % Initialize cell array with one element "A"
+    text = 'A'; % Current text is "A"
+
+    while length(words) < 32
+        newText = ''; % Initialize new text as empty
+        for i = 1:length(text)
+            switch text(i)
+                case 'A'
+                    newText = [newText 'B']; % Append 'B' to new text
+                case 'B'
+                    newText = [newText 'C']; % Append 'C' to new text
+                case 'C'
+                    newText = [newText 'AB']; % Append 'AB' to new text
+            end
+        end
+        text = newText; % Update text with the new text
+        words{end+1} = text; % Append new text to words list
+    end
+end
+
+function padovan_sequence = Padovan1(nmax)
+    padovan_sequence = zeros(1, nmax);
+    padovan_sequence(1:3) = [1, 1, 1];
+    for n = 4:nmax
+        padovan_sequence(n) = padovan_sequence(n-2) + padovan_sequence(n-3);
+    end
+end
+
+function padovan_approx = Padovan2(nmax)
+    p = 1.324717957244746025960908854;
+    s = 1.0453567932525329623;
+    padovan_approx = floor(p.^(-1:nmax-2) / s + 0.5);
+end