[ *January 22, 2002* ]

Bringing democracy into the Rabbit series

John McNamara

Take the Rabbit series set out in Fibonacci length substrings

**1**

0

11

010

11011

01011010

1101101011011

010110101101101011010

1101101011011010110101101101011011

It is undemocratic! There are more ones than zeros,

(1.618034 ones to 1 zeros approx.)

This is rectified by using its undemocratic self modified

to rectify the situation. The "modified" series used was 01011010...

in other words, the normal Rabbit sequence with 0 tacked on the

beginning which is why the first "cut" is three bits and not 5.

So taking three bits for a 0, and five

bits for a 1 and operating on the original series using the modified

series, we get (using asterisks as separators), and we

"or" every second string, (i.e. swap a 0 for a 1 and vice versa):

**1**

0

1*1

010

1*101*1

0101*1010

1*101*10101*101*1

0101*10101*101*10101*1010

1*101*10101*101*10101*10101*101*10101*101*1

etc.

(incidentally showing a marvellous symmetry)

So we have **101*10101*101*10101*10101*101*10101*101*1** etc. which,

if "or"ed after one asterisk and un"or"ed after the next asterisk etc.

becomes **101*01010*101*01010*10101*010*10101*010*1** etc.,

which IS democratic.

Source : mistermac

See also related WONplate 118