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Studies on the Pea Pattern Sequence

Andre Kowacs

Abstract

In this paper we formally define the family of sequences know as "Pea Pattern". We then analyse its behaviour and conditions for fixed and periodic points. The paper ends with a list of fixed points and cycles.

Studies on the Pea Pattern Sequence

Abstract

In this paper we formally define the family of sequences know as "Pea Pattern". We then analyse its behaviour and conditions for fixed and periodic points. The paper ends with a list of fixed points and cycles.

Paper Structure

This paper contains 3 sections, 6 theorems, 42 equations, 6 tables.

Table of Contents

  1. Abstract
  2. Introduction
  3. Preliminaries

Key Result

Theorem 1

For all $x_0 \in \Sigma_k$, the sequence defined by $x_{n+1} = \mathcal{P}_k(x_n)$ converges to a fixed point or a cycle.

Theorems & Definitions (12)

  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Corollary 1
  • proof
  • ...and 2 more