From: reingold@cs.uiuc.edu (Edward M. Reingold)
Subject: Kippah patterns
Originator: reingold@emr.cs.uiuc.edu
Organization: University of Illinois, Dept. of Comp. Sci., Urbana, IL
Distribution: soc
Date: Fri, 11 Dec 1992 20:10:07 GMT

I posted this note some years ago, but since there has lately been discussion
of crocheted kippot, reposting it may be of interest.  Here are 5 patterns of
my own devising:

        a Hilbert curve pattern (base + 1 or 2 colors; easy)
        a pentomino pattern (4 colors in pattern; moderate)
        a triple braid (base + 3 colors; slightly difficult)
        a quadruple braid (base + 4 colors; quite difficult)
        an Escher six pointed star pattern (base + 4 colors; quite difficult)

All of these patterns are mathematically motivated and look quite striking.

My estimates of the difficulty comes from the various people who have
crocheted them for me over the years (I have several of each pattern),
including my daughter who is just now reaching the skill-level needed for the
"quite difficult" patterns.  If you are not too experienced, I'd stay away
from the last two.

If you pass any of the patterns on to others, I'd appreciate if you give me
credit for their design and ask that those to whom you give the patterns pass
on my name as the designer.  I'd like to hear how the kippot came out!

------------------------------Hilbert Curve----------------------------------
aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa a
a a a a a a a a a a a a a a a a a a a a a a a a a
a aaa a a aaa a a aaa a a aaa a a aaa a a aaa a a
a     a a     a a     a a     a a     a a     a a
aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa a
  a a     a a     a a     a a     a a     a a    
aaa aaaaaaa aaa aaa aaaaaaa aaa aaa aaaaaaa aaa a
a             a a             a a             a a
a aaaaa aaaaa a a aaaaa aaaaa a a aaaaa aaaaa a a
a a   a a   a a a a   a a   a a a a   a a   a a  
aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa a
    a     a         a     a         a     a      
aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa aaa a
a a   a a   a a a a   a a   a a a a   a a   a a  
a aaaaa aaaaa aaa aaaaa aaaaa aaa aaaaa aaaaa aaa

------------------------------Hilbert Curve Variation------------------------
Use the pattern above, but have one color as the base (above the curve), a
second color for the curve itself, and a third color for the base below the
curve.  The final row of the kippah should be in the third color, NOT the
first.  The choice of colors in this variation is critical: If the curve is in
a color lighter than than third color (below), the tree-like structure of the
lower part of the kippah will be emphasized.  Either choice is okay, but the
results will look radically different.

------------------------------Pentomino--------------------------------------
ccaaaaddddddddbbbbccccaaaaddddddddbbbbccccaaaaddd
ccaaaaddddddddbbbbccccaaaaddddddddbbbbccccaaaaddd
aaaaccccccddaabbbbccaaaaccccccddaabbbbccaaaaccccc
aaaaccccccddaabbbbccaaaaccccccddaabbbbccaaaaccccc
aabbddddccbbaabbccccaabbddddccbbaabbccccaabbddddc
aabbddddccbbaabbccccaabbddddccbbaabbccccaabbddddc
bbbbbbddccbbaaaaddddbbbbbbddccbbaaaaddddbbbbbbddc
bbbbbbddccbbaaaaddddbbbbbbddccbbaaaaddddbbbbbbddc
ddbbddddbbbbbbaaccddddbbddddbbbbbbaaccddddbbddddb
ddbbddddbbbbbbaaccddddbbddddbbbbbbaaccddddbbddddb
aaaaaaaaaaccccccccddaaaaaaaaaaccccccccddaaaaaaaaa
aaaaaaaaaaccccccccddaaaaaaaaaaccccccccddaaaaaaaaa

------------------------------Triple Braid-----------------------------------
   c     a     b     c     a     b     c     a   
  ccc   aaa   bbb   ccc   aaa   bbb   ccc   aaa  
 ccccc aaaaa bbbbb ccccc aaaaa bbbbb ccccc aaaaa 
b c ccc a aaa b bbb c ccc a aaa b bbb c ccc a aaa
bb   ccc   aaa   bbb   ccc   aaa   bbb   ccc   aa
bbb a ccc b aaa c bbb a ccc b aaa c bbb a ccc b a
 b aaa c bbb a ccc b aaa c bbb a ccc b aaa c bbb 
  aaa   bbb   ccc   aaa   bbb   ccc   aaa   bbb  
 aaa b bbb c ccc a aaa b bbb c ccc a aaa b bbb c 
aaa bbbbb ccccc aaaaa bbbbb ccccc aaaaa bbbbb ccc
aa   bbb   ccc   aaa   bbb   ccc   aaa   bbb   cc
a     b     c     a     b     c     a     b     c

------------------------------Quadruple Braid--------------------------------
c     d     a     b     c     d     a     b     c
cc   ddd   aaa   bbb   ccc   ddd   aaa   bbb   cc
ccc ddddd aaaaa bbbbb ccccc ddddd aaaaa bbbbb ccc
 c ddd d aaa a bbb b ccc c ddd d aaa a bbb b ccc 
  ddd   aaa   bbb   ccc   ddd   aaa   bbb   ccc  
 ddd c aaa d bbb a ccc b ddd c aaa d bbb a ccc b 
b d ccc a ddd b aaa c bbb d ccc a ddd b aaa c bbb
bb   ccc   ddd   aaa   bbb   ccc   ddd   aaa   bb
bbb a ccc b ddd c aaa d bbb a ccc b ddd c aaa d b
 b aaa c bbb d ccc a ddd b aaa c bbb d ccc a ddd 
  aaa   bbb   ccc   ddd   aaa   bbb   ccc   ddd  
 aaa b bbb c ccc d ddd a aaa b bbb c ccc d ddd a 
aaa bbbbb ccccc ddddd aaaaa bbbbb ccccc ddddd aaa
aa   bbb   ccc   ddd   aaa   bbb   ccc   ddd   aa
a     b     c     d     a     b     c     d     a

------------------------------Escher Stars-----------------------------------
bbbb  accccccc  dbbbbbbb  accccccc  dbbbbbbb  acc
bbbbbaaccccccccddbbbbbbbbaaccccccccddbbbbbbbbaacc
bbaaaaacccccdddddbbbbbaaaaacccccdddddbbbbbaaaaacc
bbaaaaaaaaccddddddddbbaaaaaaaaccddddddddbbaaaaaaa
 baaaaaaa  cddddddd  baaaaaaa  cddddddd  baaaaaaa
 aaaaaaab  dddddddc  aaaaaaab  dddddddc  aaaaaaab
aaaaaaaabbddddddddccaaaaaaaabbddddddddccaaaaaaaab
cccaaaaabbbbbdddddcccccaaaaabbbbbdddddcccccaaaaab
cccaabbbbbbbbddccccccccaabbbbbbbbddccccccccaabbbb
ccca  bbbbbbbd  ccccccca  bbbbbbbd  ccccccca  bbb
cccc  dbbbbbbb  accccccc  dbbbbbbb  accccccc  dbb
cccccddbbbbbbbbaaccccccccddbbbbbbbbaaccccccccddbb
ccdddddbbbbbaaaaacccccdddddbbbbbaaaaacccccdddddbb
ccddddddddbbaaaaaaaaccddddddddbbaaaaaaaaccddddddd
 cddddddd  baaaaaaa  cddddddd  baaaaaaa  cddddddd

-- 

Professor Edward M. Reingold                  Email: reingold@cs.uiuc.edu
Department of Computer Science                Phone: (217) 333-6733
University of Illinois at Urbana-Champaign    FAX:   (217) 333-3501
1304 W. Springfield Ave.
Urbana, IL 61801-2987  USA