Certain terms, not common in an art context, are necessary for a discussion of serial art. As yet, these terms, often abused have remained undefined. Some of the following definitions are standard, some are derived from the above investigations, the rest are tailored to specific problems of the work itself:

**Abstract System**

A system in which the physical units that are to function as objects have not been specified.

**Binary**

Consisting of two elements

**Definite Transition**

A rule taht requires at some definite interval before or after a given unit, som other unit is required or excluded.

**Grammer**

The aspect of the system that governs the permitted combinations of elements belonging to that system

**Isomorphism**

A relation between systems so that by rules of transformation each unit of one system can be made to correspond to one unit of the other

**Orthogonal**

Right angled

**Permutation**

Any of the total numbers of changes in order which are possible within a set of elements.

Probability

The ratio of the numbers of ways in which an event can occur in a specified form to the total number of ways in which the event can occur.

**Progression**

A discrete series that has a first but not neccesarily a last element in which every intermediate lement is related by a uniform law to the other**(a) Arithmetic Progression**

A series of numbers in which succeeding terms are derived by the addition of a constant number (2,4,6,8)**(b) Geometric Progression**

A series of numbers in which succeeding terms are derived bythe multiplication by a constant factor (2,4,8,16,32)

**Reversal**

An operation consisting of an inversion or upside-down turn within a series.

Rotation

An operation consisting of an axial turn within a series

Sequence

State of being in a successive order

Series

A set of sequencially ordered elements, each related to the preceding in a specifiable way by the logican conditions of a finite progression, ie. there is a first and last member, every member except the first has a single immediate predecessor from which it is derived and every member except the last a single immediate successor.

Set

The totality of points, numbers, or other elements which satisfy a given condition.

Simultaneity

A correspondence of time or place in the occurrence of multiple events.

In *Open Systems. *