Help / Phrases / 8. B. Grids
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8B. Grids
| m0=: i. | First y non-negative integers |
| m1=: Ai=: >:@i. | Augmented integers (begin at 1) |
| m2=: Ei=: i.@>: | Extended integers (0 to y inclusive) |
| m3=: Si=: -Ei@+: | Symmetric integers (-y to y inclusive) |
| m4=: grid=: +`(*i.)/ | General grid (2{y steps from 0{y by 1{y) |
| m5=: cb=: ] {. 1 _1"_ $~ >: - 2&| | Checkerboard. Try box cb 2 3 4 5 |
| m6=: box=: <"2 | Box rank 2 cells (for readable display) |
| m7=: CB=: *cb@$ | Alternate signs of atoms of y. |
| m8=: bcb=: _1&=@cb | Boolean checkerboard |
| m9=: {. 0 1"_ $~ ] + 2&|@>: | " |
| m10=: _1: ^ m9 | Checkerboard |
| a11=: syft=: (/~)(@Si) | Symmetric function tables |
| v12=: WRAP=: wrap : (wrap@]^:[) | Wrap (monad) and repeated wrap (dyad) |
| m13=: wrap=: RL@(,.(next+i.@#))^:4 | Wrap argument with successive integers |
| m14=: RL=: |.@|: | Roll table to left |
| m15=: next=: >:@(>./)@, | Next integer after largest in table |
The first four phrases give commonly useful integer lists, and the fifth allows specification of the beginning value, the step size, and the number of steps. For example:
(m0 ; Ai ; Ei ; Si) 3 +-----+-----+-------+----------------+ |0 1 2|1 2 3|0 1 2 3|3 2 1 0 _1 _2 _3| +-----+-----+-------+----------------+ (*/~ ; !/~) Si 3 +-------------------+-----------------+ | 9 6 3 0 _3 _6 _9|1 0 0 0 _1 _4 _10| | 6 4 2 0 _2 _4 _6|3 1 0 0 1 3 6| | 3 2 1 0 _1 _2 _3|3 2 1 0 _1 _2 _3| | 0 0 0 0 0 0 0|1 1 1 1 1 1 1| |_3 _2 _1 0 1 2 3|0 0 0 0 1 0 0| |_6 _4 _2 0 2 4 6|0 0 0 0 _1 1 0| |_9 _6 _3 0 3 6 9|0 0 0 0 1 _2 1| +-------------------+-----------------+ grid 3 4 5 3 7 11 15 19
Phrases 5-10 give various checkerboard patterns. Note the alternation along each axis:
box cb 2 3 4 5 +--------------+--------------+--------------+ | 1 _1 1 _1 1|_1 1 _1 1 _1| 1 _1 1 _1 1| |_1 1 _1 1 _1| 1 _1 1 _1 1|_1 1 _1 1 _1| | 1 _1 1 _1 1|_1 1 _1 1 _1| 1 _1 1 _1 1| |_1 1 _1 1 _1| 1 _1 1 _1 1|_1 1 _1 1 _1| +--------------+--------------+--------------+ |_1 1 _1 1 _1| 1 _1 1 _1 1|_1 1 _1 1 _1| | 1 _1 1 _1 1|_1 1 _1 1 _1| 1 _1 1 _1 1| |_1 1 _1 1 _1| 1 _1 1 _1 1|_1 1 _1 1 _1| | 1 _1 1 _1 1|_1 1 _1 1 _1| 1 _1 1 _1 1| +--------------+--------------+--------------+ CB i. 3 4 0 _1 2 _3 _4 5 _6 7 8 _9 10 _11
Phrase 11 is an adverb that produces function tables on symmetric arguments:
(+syft ; *syft ; !syft) 3 +-------------------+-------------------+-----------------+ |6 5 4 3 2 1 0| 9 6 3 0 _3 _6 _9|1 0 0 0 _1 _4 _10| |5 4 3 2 1 0 _1| 6 4 2 0 _2 _4 _6|3 1 0 0 1 3 6| |4 3 2 1 0 _1 _2| 3 2 1 0 _1 _2 _3|3 2 1 0 _1 _2 _3| |3 2 1 0 _1 _2 _3| 0 0 0 0 0 0 0|1 1 1 1 1 1 1| |2 1 0 _1 _2 _3 _4|_3 _2 _1 0 1 2 3|0 0 0 0 1 0 0| |1 0 _1 _2 _3 _4 _5|_6 _4 _2 0 2 4 6|0 0 0 0 _1 1 0| |0 _1 _2 _3 _4 _5 _6|_9 _6 _3 0 3 6 9|0 0 0 0 1 _2 1| +-------------------+-------------------+-----------------+
The final phrases produce spirals by wrapping a table (or by default a list or scalar) in a blanket of successive integers:
]t=: i. 2 3 0 1 2 3 4 5 (RL t) ; (WRAP 0) ; (3 WRAP 0) +---+-----+--------------------+ |2 5|6 7 8|42 43 44 45 46 47 48| |1 4|5 0 1|41 20 21 22 23 24 25| |0 3|4 3 2|40 19 6 7 8 9 26| | | |39 18 5 0 1 10 27| | | |38 17 4 3 2 11 28| | | |37 16 15 14 13 12 29| | | |36 35 34 33 32 31 30| +---+-----+--------------------+