1. µi = (xX xi) / |X| =(1/57)x k 2kxi, (1/57)k 2kxxi,k3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J L M N O P Q R S T U V 1 3 7 1 2 4 1 3 5 1 23 2 3 1 2 1 3 5 2 1 3 5 2 1 3
d e f g
9 a b c
n o
l m
j k
h i
t u
r s v w
x y z A B
C D
E N F
G H
I J K L M q
p O
P Q R
S T
U V
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000
µi = (xX xi) / |X|
=(1/57)x k 2kxi,
(1/57)k 2kxxi,k
=(1/57)k 2krcPi,k
for i=1 =(1/57)*(7*23
+24*22+35*21+23*20)
=4.3
for i=2 =(1/57)*(22*23
+35*22+35*21+33*20)
=7.35

2. story but they may have higher cost? ra,0=skin(a,1)
rx1,1,k 3 1 4 3 1 2 3 2 1
d e f g
9 a b c
n o
l m
j k
h i
t u
r s v w
x y z A B
C D
E N F
G H
I J K L M q
p O
P Q R
S T
U V
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000 K 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J L M N O P Q R S T U V 1 3 7 1 2 4 1 3 5 1 23 2 3 1 2 1 3 5 2 1 3 5 2 1 3 1 6 1 1 2 4 2 1 7 2 1 8 2 1
We note that the
ring(a,d*(k-1),d*k)
tell an even greater
story but they may have higher cost?
ra,0=skin(a,1)
ra,k=ring(a,2k-1,2k)
ring(a,d*2k-1,d*2k )
k=0... tell a great story on neighbors.
(here, d=1)
rf,a,k=ring(f,f-1a,2k-1,2k)

3. µ x y z A B t u C D r s E N F q G H I J K L M n o p O v l m P Q R j k
d e f g
9 a b c
n o
l m
j k
h i
t u
r s v w
x y z A B
C D
E N F
G H
I J K L M q
p O
P Q R
S T
U V
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000 K 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J L M N O P Q R S T U V 4 1 7 4 1 4 2 1 5 S 1 2 S 1 8 S 2 1 4 U 1 3 U 1 U 2 1

4. µ x y z A B t u C D r s E N F q G H I J K L M n o p O v l m P Q R j k
d e f g
9 a b c
n o
l m
j k
h i
t u
r s v w
x y z A B
C D
E N F
G H
I J K L M q
p O
P Q R
S T
U V
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000 K 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J L M N O P Q R S T U V T 1 6 T 1 6 T 2 1 V 1 7 V 1 4 V 2 1 6 v 1 v 1 v 2 1

5. x y z A B t u C D r s E N F q G H I J K L M n o p O v l m P Q R j k
d e f g
9 a b c
n o
l m
j k
h i
t u
r s v w
x y z A B
C D
E N F
G H
I J K L M q
p O
P Q R
S T
U V
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000 K 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J L M N O P Q R S T U V q 1 q 1 q 2 1 7 w 1 2 w 1 w 2 1 s 1 3 s 1 s 2 1

6. x y z A B t u C D r s E N F q G H I J K L M n o p O v l m P Q R j k
d e f g
9 a b c
n o
l m
j k
h i
t u
r s v w
x y z A B
C D
E N F
G H
I J K L M q
p O
P Q R
S T
U V
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000 K 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J L M N O P Q R S T U V 1 5 1 4 1 2 8 5 1 8 5 1 4 5 2 1 8 9 1 9 1 8 9 2 1

7. x y z A B t u C D r s E N F q G H I J K L M n o p O v l m P Q R j k
d e f g
9 a b c
n o
l m
j k
h i
t u
r s v w
x y z A B
C D
E N F
G H
I J K L M q
p O
P Q R
S T
U V
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000 K 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J L M N O P Q R S T U V d 1 8 d 1 9 d 2 1 4 h 1 8 h 1 9 h 2 1 4 j 1 00 9 j 1 9 j 2 1 9

8. x y z A B t u C D r s E N F q G H I J K L M n o p O v l m P Q R j k
d e f g
9 a b c
n o
l m
j k
h i
t u
r s v w
x y z A B
C D
E N F
G H
I J K L M q
p O
P Q R
S T
U V
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000 K 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J L M N O P Q R S T U V l 1 9 l 1 4 l 2 1 8 n 1 5 n 1 4 n 2 1 3

9. x y z A B t u C D r s E N F q G H I J K L M n o p O v l m P Q R j k
d e f g
9 a b c
n o
l m
j k
h i
t u
r s v w
x y z A B
C D
E N F
G H
I J K L M q
p O
P Q R
S T
U V
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000 K 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J L M N O P Q R S T U V I 1 2 I 1 3 I 2 1 7 G 1 8 G 1 5 G 2 1 7 E 1 7 E 1 2 E 2

10. µ x y z A B t u C D r s E N F q G H I J K L M n o p O v l m P Q R j k
d e f g
9 a b c
n o
l m
j k
h i
t u
r s v w
x y z A B
C D
E N F
G H
I J K L M q
p O
P Q R
S T
U V
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000 K 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J L M N O P Q R S T U V C 1 C 1 2 C 2 1 5 x 1 5 x 1 3 x 2 1 7

11. TV-countours bounded by isobars gaps of at
d e f g
9 a b c
n o
l m
j k
h i
t u
r s v w
x y z A B
C D
E N F
G H
I J K L M q
p O
P Q R
S T
U V
1111
1110
1101
1100
1011
1010
1001
1000
0111
0110
0101
0100
0011
0010
0001
0000 K 1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z A B C D E F G H I J L M N O P Q R S T U V  1 m 1 4 T 1 3 M 1 9 H 1 8 F 1 7 C 1 8 x 1 9 1 2  q 1 s 1 4 u 1
x TVX gap  p P Q O m o S T R k U l i K L J M V I n g h j f H G e c N v b F E d a D C z A y B x q r t w s
u12257
57*1
57*2
57*3
57*4
57*5
57*6
57*7
TV-countours bounded by isobars gaps of at
least 57*radial_distance_from_=(7.4, 4.3)
57*7
57*8
57*9
57*11
57*14
57*15

12. TVX