Linear Assemblies

Upon the completion of the ‘standard format’, i.e. two beats to the bar with a 0-10 tempo, is the possibility of what I term as linear assemblies, or more colloquially, 'super parquet deformations', formed by the process of ‘successive assembly’ of the units. Given that these all follow the same beats to the bar and tempo and so consequently strip length, an obvious possibility is that of extending a given deformation by simply joining one to another where the beginning/end tiles match, of 1 x 2, 1 x 3… strips. Below I show instances assembled from my archive. Note that there are also matters of aesthetics to consider; it is not simply a matter of joining admissible parquet deformations without thought. There are a numbers of aspects to consider:

1. Ideally, at each transition any one tile should not repeat, except in a special circumstance, detailed below. A lesser instance, of a 4-unit strip, is e.g. square → rectangle → pentagon → rectangle. Better would be e.g. square → rectangle → pentagon → right-angled triangles. The first instance, whilst not without merit due to its long length, is obviously unbalanced, whilst the second instance is balanced, and so better. 

2. The exception referred to is when the beginning and end of the super deformation are of the same tile e.g. square → rectangle → pentagon → square. Indeed, such types are a particular favourite. This gives a cohesion to the composition and the impression is of a self-contained strip, as against different polygons at the end. However, there is nothing wrong as such with different endings. Note that this type should be distinguished from the inferior unravelling/reversal at the midpoint which in contrast lacks imagination. Further, the possibilities arise of a ring or Möbius Band. 


To begin I show two-unit joining. Of course, the process can be continued with ever larger joins.


Two-Unit Joining


Fig. 1. Argentina Buenos Aires - Italy Rome.
Transitions from squares to rectangles to squares.
Note the cohesive same tiles at ends. Also, save for the intermediary alternate regions, note that the tiles all possess mirror symmetry, which gives added value, as against an asymmetric counterpart.

Fig. 2. Portugal Lisbon - Portugal Porto.

Transitions from four right-angled triangles within a square to rectangles in a double basket weave arrangement to squares at 45°.


Fig. 3. Portugal Porto  - Brazil Belo Horizonte
Transitions from squares at 45° to rectangles in a double basket weave arrangement to squares at 45°. Note the cohesive same tiles at ends.

More to follow.

Page Created 4 June 2021


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