Ivor the Engineer
Penultimate Amazing
- Joined
- Feb 18, 2006
- Messages
- 10,590
How many patterns of heads and tails in 1000 flips might be considered significant by a human observer?
HTHT...
HHTTHHTT...
HHHTTTHHHTTT...
HTTHTTHTTHTT...
HHTTTHHTTTHHTTT...
In general: Hxn Txm ...
where n and m are integers in the range 0 to 1000 and n + m < 1000.
Then there are sequences which have mirror symmetry or other features we feel are 'special'.
A couple of experiments to try:
1) On a spreadsheet fill a column with 1024 10-bit binary numbers from 0 to 1023 (i.e. 0000000000 to 1111111111). Put a mark by the cells which, if 0 represents tails and 1 represents heads, you feel would appear significant if representing the result of flipping a coin 10 times.
What fraction of the 1024 values appear 'special' to you?
2) Write a program to produce 100 text files consisting of 1000 characters, randomly filled with H or T.
i) What proportion of the files appear to have 'special' (sub-)sequences of H and T?
Use a compression algorithm based on the Lempel-Ziv algorithm (or one which extracts patterns from the data).
ii) Is there is a correlation between the files which compress the best and which look more 'special'?
HTHT...
HHTTHHTT...
HHHTTTHHHTTT...
HTTHTTHTTHTT...
HHTTTHHTTTHHTTT...
In general: Hxn Txm ...
where n and m are integers in the range 0 to 1000 and n + m < 1000.
Then there are sequences which have mirror symmetry or other features we feel are 'special'.
A couple of experiments to try:
1) On a spreadsheet fill a column with 1024 10-bit binary numbers from 0 to 1023 (i.e. 0000000000 to 1111111111). Put a mark by the cells which, if 0 represents tails and 1 represents heads, you feel would appear significant if representing the result of flipping a coin 10 times.
What fraction of the 1024 values appear 'special' to you?
2) Write a program to produce 100 text files consisting of 1000 characters, randomly filled with H or T.
i) What proportion of the files appear to have 'special' (sub-)sequences of H and T?
Use a compression algorithm based on the Lempel-Ziv algorithm (or one which extracts patterns from the data).
ii) Is there is a correlation between the files which compress the best and which look more 'special'?
