Nuclear tri-grams in the I Ching and Base 64 encoding in Fractint.

8 Sep 2006

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Date: Sun, 3 Sep 2006 22:07:56 -0300
From: "David Fisher" <sunfish@intercom.net>
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Subject: [Fractint] Binary system
To: "Fractint and General Fractals Discussion"
<fractint@mailman.xmission.com>
Cc: philofractal@lists.fractalus.com
If anyone is interested check out the nuclear tri-gram 
designations in the I Ching. Some are also used on the S Korean 
flag. They are a base 2 system to 64 places...from 0 to 63. Zero 
being - - used as a placeholder and --- used to designate value. 
Count from the bottom up with the bottom place being 1, next 2, 
next 4, next 8, next 16, and top 32.
These markings are ancient, but they could very well be used to 
program gates for a base 64 system since gates are either on or 
off, 0 or 1.  Comments???
David M Fisher sunfish@intercom.net

Comment:   Fractint already uses a base 64 encoding 
for the color map that it saves in parameter files. 

It uses both upper and lower case letters, digits, 
and  "`" and "_". 

Here is an example from one of Jim Muth's FoTD 
postings:

  colors=000OxzOxzKxzGxzDwz9vz5uz2tz4sz5rz7qz8pzAozB\
  nzDmzElzGkzHjzKizMhzPgzRfzTezWcyYax`_wbYvdWugVtiUs\
  lTtnSspRrRUZTWXVYWX_VZ`U`bTbdSdfRegQgdRibSk_TlYUnW\
  VpTWrRXsPYuMZwK_xI`pLYiNVbQSVSPOVMHXJSg6ak3vSRpUNj\
  WJeXFB87LJ78mO5ZG2K8BsxiyxUfcFOKurzfejTUVEIF6FC4C8\
  294ckzKRVhoaU_PFLCDX3jmnNSPvzM2YE1RA1K70D3ykoi`bVR\
  QFGDzkvj`gVRTFGEp78Q64jBW7VhKqFDaA6M5Etk7VO4zD3o92\
  `61L3MAeG9VB8L57A6xh3XMVoGteaaUPJICa`SPQICG927z16V\
  vZiTKN5Wp3NZ1EHNp2WJoLEYAAH6zd3ZKqzJ883672471260uP\
  OaIGJC8DEI6A99S3ef2VX1LO1AF06wcVz6Ki4AQ22e7U`sMTeF\
  LS7DEg9lX8_M7OB6CZI3QF2HC189058s27S8iEXeXGOGkNzOEV\
  ggYTVMEIBf`mLLPvV_gORTIIEC9eJ6SE4EA2WWLwCjCtt9ge6V\
  S3IEI`CCQ86G4nq6PU32v91W4uEB_y7ozUbpMQ`FDL7`SFRMBI\
  H79B3MlBEY77K3hU8UM5FE2AVO5ICBYs7O`3FInj5PQ2_9GB8O\
  87I57C266kztWgaGPJzzrjmdVZRFKDzzijkYVYNFKBLh0yYTS9\
  jI8V97FEpFAdB7T73H3ZVBNM7 } 

My spell checker doesn't like base 64 encoding!  ;-)
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These markings are ancient, but they could very well be used to 
program gates for a base 64 system since gates are either on or 
off, 0 or 1.
It seems to me that binary encoding is the most 
direct way to map numerical digits onto a two- 
valued electronic gate system.  How one 
conveniently *views* these binary digits is quite 
another matter.  

For a long time (in the DEC PDP-11 world 
at least) binary numbers were printed in octal to 
(save space? and paper?) and enhance understanding 
over printing the binary number.  Mainframe systems 
seemed to like to encode binary numbers in hex, 
which took a little getting used to, but many people 
are comfortable using this now.  We even have a 
new phrase in the language now -- "hex dump."

Its very convenient that two hex digits exactly 
encode one byte, the smallest addressable memory 
unit on most machines.

But I would think that having to remember the 
significance of 22 or 54 letters (case would be 
important) for base 32 or 64 (instead of just 
A-F for hex) would be an almost insurmountable 
challenge. 

 - Hal Lane

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Hal Lane

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