# a pattern in chaos?

• September 17th, 2011, 10:18 AM
luxtpm
a pattern in chaos?
i take any binary number and transfrom it into a new number by comparing each digit with the next and the last one with the first, it can be equal , e or disiqual, d

for example the number 0101 in the first transformation becomes dddd and in the second transformation eeee

well any binary number eventually transforms to all equal after a number of this transformations

check it out:

http://i40.photobucket.com/albums/e2...onlocality.jpg

now what should be the next step?
• September 18th, 2011, 04:43 PM
MagiMaster
Either try it with more digits, get the computer to do it for you, or prove (or disprove) your hypothesis.
• September 20th, 2011, 05:59 PM
billiards
Interesting observation. It's not really "chaos" though is it?

Can you see a reason for this behaviour?
• September 20th, 2011, 06:10 PM
billiards
It doesn't work for 5 digits.

try: deeed.

Also 6 digits, try: deeeed. Doesn't work either.
• October 9th, 2011, 01:55 PM
luxtpm
i think this only works with a number of digits power of 2
• October 9th, 2011, 02:32 PM
luxtpm
hey i think this could be used to compress info:

eeeeeeee has one transformation so this number is expressed as 000 theres one of this
dddddddd has one transformation so its expressed as 001 theres one of this
dededede has two transformation so its expressed as 010d theres 2 of this
deeddeed has 3 transformation so its expressed as 011dd therse 4 of this
deeedeee has 4 trans so its 100ddd theres 8 of this

ans so on till it gets 111dddddd theres 128 of this
• October 9th, 2011, 02:38 PM
luxtpm
normally to express 256 numbers you need 8 lines of code

with this youre using:

3+3+4*2+5*4+6*8+7*16+8*32+9*64 all divided by 256=

4.0078 lines of code :)