Data update

Task/Padovan-sequence/R/padovan-sequence.r

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+# Function to calculate Padovan sequence iteratively
+padovan_sequence <- function(n) {
+  recurrences <- numeric(n)
+  recurrences[1:3] <- c(1, 1, 1)
+  if (n > 3) {
+    for (i in 4:n) {
+      recurrences[i] <- recurrences[i-2] + recurrences[i-3]
+    }
+  }
+  recurrences
+}
+
+# Function to calculate Padovan floor
+padovan_floor <- function(aN) {
+  PP <- 1.324717957244746025960908854
+  SS <- 1.0453567932525329623
+  floor((PP^(aN - 1)) / SS + 0.5)
+}
+
+# Function to create L-system
+create_l_system<- function() {
+  words <- c("A")
+  text <- "A"
+
+  while (length(words) < 32) {
+    text <- strsplit(text, "")[[1]] # Split the string into a list of characters
+    text <- sapply(text, function(char) {
+      if (char == "A") {
+        return("B")
+      } else if (char == "B") {
+        return("C")
+      } else if (char == "C") {
+        return("AB")
+      }
+    })
+    text <- paste(text, collapse = "") # Collapse the list back into a single string
+    words <- c(words, text) # Append the new word to the list
+  }
+
+  words
+}
+
+
+# Main script
+num_terms <- 64
+padovan_seq <- padovan_sequence(num_terms)
+floors <- sapply(0:(num_terms-1), padovan_floor)
+
+cat("The first 20 terms of the Padovan sequence:\n")
+cat(padovan_seq[1:20], sep=" ", end="\n")
+cat("\n")
+
+cat("Recurrence and floor functions agree for first 64 terms?", all(padovan_seq == floors), "\n\n")
+
+words <- create_l_system()
+
+cat("The first 10 terms of the L-system:\n")
+cat(words[1:10], sep=" ", end="\n")
+cat("\n")
+
+cat("Length of first 32 terms produced from the L-system match Padovan sequence? ")
+word_lengths <- sapply(words, nchar)
+cat(all(word_lengths[1:32] == padovan_seq[1:32]))