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Interesting patterns for HP-42S - Tom Grydeland - 03-06-2012
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 }
00 { 344-Byte Prgm } Re: Interesting patterns for HP-42S - C.Ret - 03-06-2012
Quote:[...]
May I suggest RCL ST X ?
Re: Interesting patterns for HP-42S - Tom Grydeland - 03-06-2012
yes, that did occur to me after posting. It works, but uses the same # of bytes.
Re: Interesting patterns for HP-42S - C.Ret - 03-06-2012
Exact. No byte are spared here! Your code triggers me enough to let me try to observe your curious and highly symmetrical pixel patterns. I have adapt your code to my HP-28S to take advantage of the larger LCD screen (double size in row compare to HP-42S).
« 64 STWD @ Use full size binary words Usage, enter 0, 1 or 5 and press [ DPP ] menu key to see corresponding doubly-periodic pixellated patterns full screen (press [ ON ]+[ L ] to online-print screen).
I am now one the way to code other high symmetrical 8x8 pixel patterns.
Re: Interesting patterns for HP-42S - Tom Grydeland - 03-07-2012
Very nice! I don't have a 28S, so I cannot try your programs, but the output looks exactly correct. The x48 emulator works for building the string, but it doesn't like the string argument to "->LCD" -- I haven't tried particularly hard, so I might have missed some subtlety. The larger screen of the 28 could also be used to tile up the pattern, ie use 2x2 screen pixels as the basis for the pattern. Not exactly sure what kind of bit twiddling would turn the nybble "abcd" into "aabbccdd", perhaps a look-up table would be best?
I have some 2537 patterns of this weight and size (i.e. 4 of every 8 pixels are black, starting anywhere and counting horizontally, vertically or diagonally) of which 919 have more than one symmetry. They are not coded up as hexadecimal strings, however (searches started out with patterns of other sizes), but I should be able to recode to hex-strings without too much trouble.
Re: Interesting patterns for HP-42S - Marcus von Cube, Germany - 03-07-2012
Tom, the 48 series has a more evolved graphic object concept. Hunt for GROB in the documentation!
Re: Interesting patterns for HP-42S - Tom Grydeland - 03-07-2012
Here are some more interesting patterns for you to try, in hex form:
#17A33AD8C68D6C71h |