- 294 -Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory 
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can be generated with an arbitrary complexity, it was necessary to define a circular form which is open to any object compoundness.

9.1 Satellites

The essential components of such an object type are

  • the concrete multimedia attributes, such as spatial position, color, sound, etc., and
  • the circular architecture for the unlimited extensibility.


PIC


Figure 7: Satellite Form.


The object form therefore is set to Sat:.Limit(Geo,SatList). On the one hand, Geo implements the concrete multimedia attributes, whereas SatList realizes the circular architecture. The Geo component is a conjunction (limit) Geo:.Limit(URL,RTC) of space-time-coordinates (RTC) and a URL for internetrelated data URL:.Simple(Ts<ASCII > ) in string form as provided by the monoid Z -algebra Ts<ASCII >  over the ASCII  characters. The RTC component is the conjunction of these spaces: Translation, Rotation, Scaling, Color, Texture, and Sound.

Each such space-time coordinate consists of a powerset with each element of the type Limit[Limit[R , R ], Ts<ASCII > ] with two real values defining the interval of validity of the belonging string. It is important that these data are given as string combinations in Ts<ASCII > , since one is allowed to implement complex formulas which describe the way, how these coordinates are related to the input coordinates of the folding vectors Hi . For example, the angle can be given as an expression  x f = 2 + exp(- lambda *y) . Here, three of the vector coordinates of Fi are associated with


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- 294 -Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory