Chaos Theory Simply Explained (Basic Fractals/Chaos Series)

This is a concise article detailing mathematical equations showing when and where chaos occurs in linear algebraic equations and systems of linear simultaneous algebraic equations. The approach used is very simple and easy to understand by readers. Instead of using quadratic equations like the logistic equation to study chaos theory, we use simple linear equations for this purpose. The article starts with a single simple linear equation and ends with a system of two simultaneous linear equations. The conditions under which chaos occurs in linear equations are precisely investigated using several examples. The derivation of all necessary equations is shown in great detail. This article is aimed at the novice who is just starting his or her study of chaos and chaos theory. The reader is expected to know the basics of algebra at an elementary level.