Parquet Deformations of David Bailey Below I show some examples of my own parquet deformations that I consider to be (or are largely) ‘aesthetic’, from my archive. These number about 100 works, but possibly extending to about 200 (they are in various incarnations). These are mostly square-based, with on occasion on equilateral triangles and hexagons (not shown here yet). These are of a variety of dates (I return to the study ad hoc), from 1987 onwards, but are mostly of 1993, or at least the latter is of a concerted period of study of that year. These were originally hand-drawn, and of which I have latterly computer redrawn in Rhino, of February-April 2021. Note that this page is very much a work in progress; the final presentation and format is to be decided. Since its instigation in February 2021, the page has developed and changed considerably. With time, less change, upon a decided arrangement that will evolve, will occur. As I am in the process of redrawing the existing hand-drawn examples in Rhino, I will add these here at short intervals upon completion. The present format is of a parquet deformation followed by some brief text. This concerns a unique identifier, of ‘country and towns’ (this ‘oddness’ is explained below), the original date of drawing (which enables me to find the parquet deformation easily in my chronologically arranged files! Further, not all of these were drawn out as a finished work at the time, which complicates matters somewhat. Be that as it may, the date given is at least an indication of when that work was at least initiated or in some recognisable form as to the page here) I then add the date of when it was redrawn in Rhino. Finally, I describe the transition, e.g. from squares to rectangles, with a general commentary, with later more detailed and expansive text to follow in due course. Identifying/referencing each work is (perhaps surprisingly) problematic. I have so many that it is impractical to name/title these in the same imaginative way that Huff did with his students' work. A simple (and obvious) description of the beginning and end tiles, e.g. squares to right-angled triangles soon runs into repeats, with confusion as to which deformation thus arises. What is needed is a unique identifier. An obvious possibility is simply ‘parquet deformation 1, 2, 3..’. etc. However, in practice, there are problems here. As alluded to above, there is no strict order of sequence. Some are incomplete, in sketch form. Some are of a photocopied sheet of a grid filled in. Others are a finished drawing from yesteryear from a sketch. Some are of a second generation i.e. grid to parquet deformation, and then an addition. Confusion personified! To this end, I retain an old idiosyncratic system I used from my earliest days, likely much to the chagrin of any mathematician reading this! As each instance overwhelmingly follows a typical process of an ‘open grid’ and subsequent ‘filling-in’ (to greater (second generation) or lesser (first generation) degrees, I use a two-part system, where I title the open grid after a country, with the ‘filling-in’ of towns/cities thereof. For example Canada (grid) - Ottawa (filling-in); Canada - Banff etc. Although not strictly mathematical, it makes referring to any specific parquet deformation and its underlying grid much easier than trying to remember a strictly mathematical procedure e.g. instance 64 (grid) and what 64a, 64b, 64c (variations) represents, or, even more involved, with second generation instances, e.g. 64a(i)!. Of course, I could have used any other ‘two-part’ system; there is nothing unique about the ‘country and town’ system. Below I show some examples of my own that I consider ‘aesthetic’ (dating from 1987), numbering about 100, but possibly extending to about 200 works. These are mostly square-based, with on occasion based on equilateral triangles and hexagons. Note that this is very much a work in progress; I am in the process of redrawing existing hand-drawn examples in Rhino, of which I will add here at short intervals, with later accompanying text. Inventory. Largely for my own record keeping! I have so many parquet deformations, with many variations, that keeping track of what I have added to the page is inconvenient. Further, everything is in a state of flux, with drawing in Rhino learnt as I go along. The listing numbering is to be considered as first attempt at a degree of order. This at least enables me to see at-a-glance what I have added without time-consuming and (ever increasing) scrolling. 1. France (Old) To be renamed
2. France - Paris. To be renamed.
3. France - Lyon
France - Metz
4. Argentina - Buenos Aires The Parquet Deformations
Transitions from square to right-angled triangles (with rectangles mid-stream). This is in particular elegant, and a favourite. Described as minimalist.   Transitions from right-angled triangles to right-angled triangles (with squares mid-stream). A curious feature is the lines at 45° throughout. Another interpretation is Paris rotated 180° and superimposed. Elegant.  Transitions from squares to parallelograms (derived from the square). A curious feature is that the transition forms the same tile at 180° before resolving as single parallelograms.  Transitions from squares to rectangles, at 45°. This is in particular elegant, and a favourite. Described as minimalist.  5. Originally 28 June 1993. Redrawn in Rhino 2021. Transitions from squares at 45° to right-angled triangles, set within a subdivided square  6. Mexico - Acapulco. Originally 28 June 1993  7. Canada - Ottawa. Originally 28 June 1993. Redrawn in Rhino 2021 Transitions from squares of two sizes to Greek crosses.  8. Canada - Banff. Originally 28 June 1993. Redrawn in Rhino 2021  9. Canada. 2 March 2021.  10. USA - New York. Originally 28 June1993. Redrawn in Rhino 2021   12. USA - Minneapolis. Overlay. New 9 March 2021     16. USA - Baltimore Subdivided (New). 11 March 2021  17. French Guiana - Cayenne. Originally 28 June 1993. Redrawn 10 March 2021* Transitions from squares to four right-angled triangles within a square.    Transitions from squares to small squares at 45°.  Transitions from squares to two right-angled triangles set within a square. However, the transition overall lacks elegance, with intermediate tiles of no particular aesthetic. It's only merit is the beginning and end transition itself, as a specific design solution. However, as can be seen on this page, I am not short of such specifics!  22. Libya - Misurata. Originally 2 July 1993. Redrawn in Rhino 11 March 2021* Transitions from squares to squares, with symmetrical intermediary tiles.  Transitions from parallelograms to squares. However, the transition overall lacks elegance, with intermediate tiles of no particular aesthetic, of 'elongated' tiles without symmetry. It's only merit is the beginning and end transition itself, as a specific design solution.  24. Ecuador - Ambato. Originally 28 June 1993. Redrawn in Rhino 12 March 2021 Begins and ends with the same square tiles, at 45°, as a consequence of its natural cycle (as against an inferior unravelling at the middle, back to square), which gives a pleasing cohesion.  25. Ecuador - Cuenca. New. Drawn in Rhino 12 March 2021 An unusual instance, of overlapping lines at the right-hand side  26. Belgium - Brussels. Originally 1993. Redrawn in Rhino 15 March 2021. (No. 6 on main page) Transitions from rectangles at 45° to two right-angled triangles within a square. Very nice, minimalistic, a favourite.  Transitions from squares to two right-angled triangles within a square. Very nice, minimalistic, a favourite.  28. Brazil - Rio De Janeiro. Originally 21 June 1993. Redrawn in Rhino 16 March 2021.* Transitions from squares to squares at 45°  Transitions from double basketweave to squares at 45°. Very nice, with the pleasing feature of the tiling overlapping at 90°.  Transitions from a double basketweave tiling to four right-angled triangles set within a square.  31. Brazil - Sao Paulo. Originally 23 June 1993. Redrawn in Rhino 16 March 2021. Composed by suitably subdividing Brazil - Rio De Janeiro Transitions from a double basketweave tiling to squares at 45°.  Transitions from squares to squares and four right-angled triangles with a square at 45°.  Adjusted FW.jpg) Transitions from double basketweave to two sizes of right-angled triangles in an 'involved' arrangement that is hard to describe!  FW.jpg) Transitions from double basketweave to two sizes of right-angled triangles in an 'involved' arrangement that is hard to describe!  35. Venezuela - Barquisimeto. Originally 1989? Redrawn in Rhino 25 March 2021. Composed by suitably subdividing Venezuela - Caracas Transitions from a double basketweave tiling to large and small right angled triangles within two different sizes of squares 36. Venezuela - Mataray. New. 25 March 2021. Composed by suitably subdividing Venezuela - Caracas Transitions from a double basketweave tiling to large and small right angled triangles within two different sizes of squares   40. England - London. Originally 23 June 1993. Redrawn in Rhino 26 March 2021. (No. 10 on main page)  41. England - Lincoln. New. Drawn in Rhino 26 March 2021. Composed by suitably subdividing England - London.      45. Portugal - Porto. Originally 2 July 1993. Redrawn in Rhino 30 March 2021 (Funchal Subdivided) (No. 9 on main page) Aesthetic. This shows the minima to maxima of the Cairo tiling.  46. Portugal - Faro. Originally 2 July 1993. Redrawn in Rhino 30 March 2021 (Funchal Subdivided)  47. Portugal - Lisbon. Originally? Redrawn in Rhino 30 March 2021 (Funchal Subdivided) (No. 7 on main page) Aesthetic. Simple, but elegant.   49. Suriname - Paramaribo. Originally 28 June 1993. Redrawn in Rhino 31 March 2021*  50. Suriname - Lelydorp. Originally 28 June 1993. Redrawn in Rhino 31 March 2021 Transitions from parallelogram to parallelogram (of two right angled triangles), rotated 90°).  51. Tunisia - Bizerte. New. Drawn in Rhino 2 April 2021 Transitions from parallelograms to rectangles at 45°.  52. Tunisia - Hammamet. New. Drawn in Rhino 2 April 2021 Transitions from reflected parallelograms to rectangles at 45°.  53. Tunisia - Kairoaun. New. Drawn in Rhino 2 April 2021 Transitions from squares to chevrons.  54. Tunisia - Sousse. New. Drawn in Rhino 2 April 2021* Transitions from squares to rectangles at 45°.  55. Tunisia - Tunis. New. Drawn in Rhino 2 April 2021* Transitions from squares to rectangles at 45°.  56. Cuba - Camaguey. Originally 28 June 1993. Redrawn in Rhino 17-18 April 2021 Transitions from pinwheels to four right angled triangles.  57. Cuba - Havana. Originally 28 June 1993. Redrawn in Rhino 17-18 April 2021   59. Cuba - Veradero. New. Drawn in Rhino 17-18 April 2021  60. Italy - Rome. Drawn in Rhino 17-18 April 2021* (No. 4 on main page)  61. India - Delhi. Drawn in Rhino 12 April 2021   63. Romania - Bucharest. Drawn in Rhino 13 April 2021 (No. 8 on main page)   65. Romania - Timisoara (same as England, London!). Drawn in Rhino 13 April 2021 (No. 10 on main page)    68. Switzerland - Geneva. Drawn in Rhino 5 April 2021   70. Netherlands - Amsterdam. Drawn in Rhino 9 May 2021. (No. 1 on main page)  Transitions from parallelograms to rectangles at 45°. Note the lines at 45° throughout the composition. Very nice!  72. Sudan - Atbara. New. Drawn in Rhino 12-13 May 2021 Transitions from squares to chevrons. Also see No. 53. Tunisia - Kairouan for another transition  73. Sudan - Kadugli. New. Drawn in Rhino 12-13 May 2021 Transitions from squares to rectangles/concave par hexagon.  Transitions from squares and parallelograms to rectangles at 45° in a herringbone arrangement.  75. Mozambique - Lichanga. New. Drawn in Rhino 17-18 May 2021 Transitions from L-Tromino at 45° to par hexagons. 76. Mozambique - Biera. New. Drawn in Rhino 17-18 May 2021 77. Mozambique - Pemba. New. Drawn in Rhino 17-18 May 2021 78. Mozambique - Matola. New. Drawn in Rhino 17-18 May 2021  79. Austria - Vienna. Originally January 2021. Redrawn in Rhino 6 April 2021 Transitions from squares to rectangles at 45°.  80. Australia - Adelaide. New. Drawn in Rhino 16 April 2021 Transitions from parallelograms to two right-angled tringles within a square.  81. Bulgaria - Varna. New. Drawn in Rhino 24 May 2021 Transitions from parallelograms to chevrons. Specific Transitions The above collection can be used to select as according to specific transitions, such as square to right-angled triangles, and see all the examples in any one transition, with the aim in mind of selecting a best, generally based on symmetry. Each specific transition has a brief commentary as to its merits (or otherwise!). Each instance is titled in a dual manner, e.g. ‘Square to two right-angled triangles within a square/Two right-angled triangles within a square to square’. Simply stated, the reverse is possible by simply rotating the parquet deformation 180°, and so rather than in effect duplicating existing examples resulting in a very long listing, I thus show this dual ordering. Inventory 1. Square to two right-angled triangles within a square/Two right-angled triangles within a square to square (4) 2. Square to Rectangle at 45°/Rectangles at 45° to Squares (4) 3. Square to Square (Self Dual) (1) 4. Square to four right-angled triangles within a square/Four right-angled triangles within a square to a square 5. Square to Parallelogram/Parallelogram to Square 6. Square to Small Square at 45°/Small Square at 45° to Square (2) 7. Rectangles at 45° to two right-angled triangles within a square/Two right-angled triangles within a square to rectangles at 45° (1) 1. Square to two right-angled triangles within a square/Two right-angled triangles within a square to square (4)  France - Paris Libya - Tripoli 2. Squares to Rectangles at 45°/Rectangles at 45° to Squares (4) Tunisia - Tunis Italy - Rome 3. Square to Square (1) 4. Square to four right-angled triangles within a square/Four right-angled triangles within a square to a square (2) French Guiana - Cayenne French Guiana - Cayenne Reflected horizontally 5. Square to Parallelogram/Parallelogram to Square .jpg) 6. Squares to Small Squares at 45° (2) Brazil - Rio De Janeiro Large square at 45° to Four Right-Angled triangles/Four Right-Angled triangles to large square at 45° (1)  Rectangles at 45° to two right-angled triangles within a square/Two right-angled triangles within a square to rectangles at 45° (1) Belgium - Brussels Page created 18 February 2021. Last Updated 19 May 2021 |
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