There are doubly-periodic pixellated patterns in which the frequencies of lit to unlit pixels are equal across all rows, columns and diagonals (left and right) of the pattern. When the basic pattern is of size 8, the frequencies can be equal. Looking for particular symmetries can lead the way to some strikingly beautiful patterns. I was curious to find out how compactly I could represent these in the HP-42S, and came up with the program listed below. (Rv is roll down, * is multiply).

Enter a number from 0 to 10 in ST X and XEQ "DPP". (only 0, 1, and 5 shown below, to save a bit of typing)

The underlying mathematics for the pattern search was published by prof. Ben Johnsen in the norwegian mathematical journal Normat in 2001. The paper (in Norwegian) is not available on-line, but I can provide copies upon request.

A small selection of patterns with other sizes and symmetries is shown in this album

00 { 46-Byte Prgm }

01 LBL "PSHOW"

02 CLLCD

03 ALENG

04 1e-5

05 *

06 1.131

07 +

08 STO 00

09 LBL 01

10 1

11 RCL 00

12 AGRAPH

13 X<>Y

14 8

15 +

16 X<>Y

17 AGRAPH

18 +

19 CLX

20 ISG 00

21 GTO 01

22 END

00 { 344-Byte Prgm }

01 LBL "DPP"

02 GTO IND ST X

03 LBL 00

04 3903507479

05 3895678231

06 GTO 96

07 LBL 01

08 4036562913

09 1013367582

10 GTO 96

...

23 LBL 05

24 4039905177

25 4029878118

26 GTO 96

.... (add more patterns here, if so desired)

46 LBL 96

47 CLA

48 XEQ 97

49 Rv

50 XEQ 97

51 XEQ "PSHOW"

52 RTN

53 LBL 97

54 4

55 STO 00

56 Rv

57 LBL 98

58 XEQ 99

59 DSE 00

60 GTO 98

61 RTN

62 LBL 99

63 ENTER

64 ENTER (if anyone know a 1-instruction DUP which does not disable stack lift, tell me)

65 255

66 AND

67 XTOA

68 Rv

69 8

70 ROTXY

71 END