51–60 of 80 posts
Could there be a number, such that for certain interesting data, you can compress the data more than normally achiveable, by indexing into the number? I feel this should not be possible, but I don't know how to proove it without a circular argument about entropy. On the other hand, if you make a string of common byte sequences, a couple GB long, and distribute it with every PC... then you surely can achive hyper comp…
With acknowledgement to the palette hack discussed in the other comments, I still think there's a ton of value in this. So often, people observe patterns in nature that appear to be so unlikely as to be by design. I have family members that are superstitious: if a light flickers at the same time that they mention a recently deceased loved one, it must be "a sign". Similarly, they will point to some overwhelmingly unl…
Earlier quoted context omitted.
Not exactly the same thing, but related: I think everyone believes Pi is a Normal Number, but it isn’t proven. https://en.m.wikipedia.org/wiki/Normal_number I think if we could prove Pi is normal, we could probably also prove your statement to be true (but I’m not sure about that)
Normal is actually a stronger claim than "contains any finite string as a substring". That normal numbers contain any finite string as a substring is a straightforward consequence of the infinite monkey theorem: https://en.wikipedia.org/wiki/Infinite_monkey_theorem To see that the converse does not always hold, you could take something like the Champernowne constant https://en.m.wikipedia.org/wiki/Champernowne_consta…
Dumb question, but is any arbitrary string of digits with length N, somewhere in pi?
Even if you could find an arbitrary file inside pi, to even describe the offset into pi, you would probably need an even larger file to just store the offset number, in most cases?
Earlier quoted context omitted.
I am really curious about the search algorithm. I love the palette hack, how did you find candidates to then start searching through the possible palettes? I can sort of think of: 1) Collapse the colours in the palette to the minimum necessary to be seen as "Waldo". The more slack in the gif palette the better - 24bit colour vs 16 colours (or fewer) in the starting image? 2) For each substring in Pi, map the hex valu…
Another pass. We're looking for a substring with the largest number of unique values. If we have unique values, we can paint each value with a colour close enough to the expected value that humans will see them as the same. Maybe?
What I do is search for substrings with the fewest repeated bytes that don't match the target pattern. I prioritize first minimizing conflicts between light (white and tan) vs. dark (black and red). Reducing other conflicts is a tie-breaker.
The featured gif has 79 "mismatched" pixels out of 494, by the black/white metric. I've found candidates with as few as 75, but subjectively I didn't think they looked as good.
With acknowledgement to the palette hack discussed in the other comments, I still think there's a ton of value in this. So often, people observe patterns in nature that appear to be so unlikely as to be by design. I have family members that are superstitious: if a light flickers at the same time that they mention a recently deceased loved one, it must be "a sign". Similarly, they will point to some overwhelmingly unl…
> What are the odds? Assuming pi is normal [1], the probability of any bit string occurring in pi is 1. [1] https://en.wikipedia.org/wiki/Normal_number