Data update

Task/Padovan-sequence/Elixir/padovan-sequence.elixir

@@ -0,0 +1,55 @@
+# Padovan sequence as a Stream
+defmodule Padovan do
+  def stream do
+    Stream.resource(
+      fn -> {1, 1, 1} end,
+      fn {a, b, c} ->
+        next_value = a + b
+        {[a], {b, c, next_value}}
+      end,
+      fn _ -> :ok end
+    )
+  end
+end
+
+# Padovan floor function
+defmodule PadovanFloorFunction do
+  @p 1.324717957244746025960908854
+  @s 1.0453567932525329623
+
+  def padovan_f(n), do: trunc((:math.pow(@p, n - 1) / @s) + 0.5)
+end
+
+# Calculate and print the first 20 elements of the Padovan sequence and the floor function
+padovan_sequence = Padovan.stream() |> Enum.take(20)
+padovan_floor_function = Enum.map(0..19, &PadovanFloorFunction.padovan_f(&1))
+
+IO.puts("Recurrence Padovan: #{inspect(padovan_sequence)}")
+IO.puts("Floor function:     #{inspect(padovan_floor_function)}")
+
+# Check if the sequences are equal up to n
+n = 63
+bool = Enum.map(0..(n-1), &PadovanFloorFunction.padovan_f(&1)) == Padovan.stream() |> Enum.take(n)
+IO.puts("Recurrence and floor function are equal up to #{n}: #{bool}.")
+
+# L-system generator as a Stream
+defmodule LSystem do
+  def stream(axiom \\ "A", rules \\ %{"A" => "B", "B" => "C", "C" => "AB"}) do
+    Stream.iterate(axiom, fn string ->
+      string
+      |> String.graphemes()
+      |> Enum.map(&Map.get(rules, &1, ""))
+      |> Enum.join()
+    end)
+  end
+end
+
+# Calculate and print the first 10 elements of the L-system
+l_system_sequence = LSystem.stream() |> Enum.take(10)
+IO.puts("First 10 elements of L-system: #{l_system_sequence |> Enum.join(", ")}")
+
+# Check if the sizes of the L-system strings match the Padovan sequence
+n = 32
+l_system_sizes = LSystem.stream() |> Enum.take(n) |> Enum.map(&String.length/1)
+bool = l_system_sizes == Padovan.stream() |> Enum.take(n)
+IO.puts("Sizes of first #{n} L_system strings equal to recurrence Padovan? #{bool}.")