Langlet's Atlas of Natural Shapes 
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 Langlet's Atlas of Natural Shapes

NB.
NB. Those of you who read the preceedings of APL93 recall Langlet's
NB. Atlas of Natural Shapes. Well, here is the translation into j 7.0.
NB. For example :
NB.

NB. 255   0
NB. 255 255
NB.   0 255
NB.   0   0
NB. 255   0

NB. 255  93
NB.  49 243
NB. 128   0
NB. 206 243
NB.   0  93
NB. 255  93
NB.
NB. Experiment with plotting combinations such as :
NB.   4 _1 shapes 3 17
NB.   3 _1 shapes 3
NB.

shapes =. 0 : 0
0 0 shapes y.
:


 NB. 0 { s is symmetry
 NB. 1 { s designates transformation type, helical(_1), none(0), and cognical(1)
 NB. 0 { n is the recursive order (though recursion is not explicitly used)
 NB. 1 { n is the differential integro number
 b =. ,0
 d =. 0.5
 t =. 2 4 $ 0 1 0 1 1 1 0 1

 i =. >. d * $ b
 b =. i {. b
 l =. {. 0 < k =. {. }. s
 s =. {. 1&{. s

 l =. 0 > k
 s =. s + 6 * s = 0

 m =. (2 1)&o. o. 2 % s
 m =. m , |. 1 _1 * m
 i =. s,$ k =. m =. 2 2 $ m
 i =. 0
 t =. k
 m =. ,: m
 sm1=. s - 1
l0)
 m =. m , (t =. t +/ .* k)
 sm1 =. <: sm1
 $.=. >(sm1 >0){l1 ; l0
l1)
 b =. {. ~:/\ ^: (1&{. 1&}. n) b
 k =. s * $ b
 k =. k * >: i =. ~:/ k $ b
 k =. |. 2 , <. k + d
 m =. k $ ; 0&{"1 m
 i =. >: 2&{. <. s * d
 t =. s | <: _1&|. +/\((0&{k)$b){i
 t =. t { m
 t =. +/\ t
 k =. $ t =. <. d + t * i =. 255  NB. use any factor
 t =. ; t - k $ <./ t
 k =. i % >./ t
 t =. <. d + t * k
 t =. t, 2 {. t
)

cog =. 0 : 0
 n =. q =. {. $ b =. y.
 f =. g =. ~:/\ q {. 1
l0)
 f =. f, g=. ~:/\ g
 n =. <: n
$.=.>(n>1){l1;l0
l1)
 g =. (q,q) $ f
 r =. g ~:/ . *. |. b
)

hel =. 0 : 0
 n =. q =. {. $ b =. y.
 f =. g =. ~:/\ q {. 1
l0)
 f =. f, g=. ~:/\ g
 n =. <: n
$.=.>(n>1){l1;l0
l1)
 g =. (q,q) $ f
 r =. |."1 g ~:/ . *. b
)



Sat, 01 Feb 1997 13:15:12 GMT  
 
 [ 1 post ] 

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