Notation

Sequence Notation

What I refer to as “sequences” take the general form:

$(variable name)_{(integer)}$

It is generally used when referring to iterations. We start with an initial value $(variable name)_0$ , that will determine the rest of the sequence. For example, if $x_{n+1} = 2*x_n$ , with $x_0 = 2$ , then $x_1 = 4$ because $x_{0+1} = 2*x_0$ . Then $x_2 = 8 \because x_{1 + 1} = 2*x_1$ .

Time Derivative Notation

A “time derivative” is a somewhat-symbol of the form:

$\frac{d(variable name)}{dt}$

It is often used in 3D chaotic attractors and some 2D. It does not necessarily need an initial value, but most of the time it will not progress if every coordinate is 0. Take $\frac{dx}{dt} = 2*x^2 - 3*x$ , it deals less with iterations and more with time. In this case $dx$ means “change of $x$ ”, and $dt$ = “change in time”. In other words, it is the change of $x$ as time, $t$ , progresses. The fraction form can somewhat be exploited and changed to $dx = (2*x^2 - 3*x)*dt$ , so lower values of $dt$ mean subsequent slower changes of $t$ .