Burning Ship Fractal

Post by schoen » Mon, Sep 26, 2016, 6:10 PM UTC

wyager wrote: post #18

jerf wrote: post #15

Earlier quoted context omitted.

"Where does all that 'entropy' come from?" Your scare quote suggests you may already know this, but for the benefit of others, the answer is that there isn't any. Fractals may look visually complicated, but their information content is fully captured by the routines used to generate them, which include the formula and the coloring system being used. This is one of the ways in which "information" is a highly counter-i…

Yes, that is what I mean. Why is there a disconnect between the complexity of the compact description and the naive description? Why are simple expressions not simple in all "natural" representations? This is not addressable with the contrived example of "you can create an encoding scheme that reduces an arbitrarily complex description to an arbitrarily short identifier". After all, this is not a constructed compress…

Post by Grue3 » Mon, Sep 26, 2016, 6:16 PM UTC

wyager wrote: post #19

andrewflnr wrote: post #17

Earlier quoted context omitted.

While "real" numbers are indeed weird, I don't think that's the real explanation here. There are lots of small programs with complex output that have nothing to do with real numbers. If someone gave you one of these programs without telling you what it was for, real numbers would at best be a useful abstraction (bear in mind that there are no actual "real numbers" here, only finite bit-strings). But it might turn out…

But computing machines aren't unpredictable. They are very predictable. They appear to pull complex structure out of the aether. Perhaps the interesting thing is that the set of n-bit programs expands to only 2^n possible outputs. Why are some finite number of infinite-length outputs accessible, but not others? Why does nature favor those sequences?

Post by [deleted] » Mon, Sep 26, 2016, 6:30 PM UTC

quarterto wrote: post #14

iverjo wrote: post #10

Fractals can be drawn by surprisingly small amounts of code. For example, this mandelbrot fractal is implemented in 122 characters of JavaScript: https://www.dwitter.net/d/123 I wouldn't be surprised if the burning ship fractal could be coded on dwitter (i.e. with 140 characters or less) as well

Just need to add a Math.abs: https://www.dwitter.net/d/457

Post by gerbilly » Mon, Sep 26, 2016, 7:20 PM UTC

wyager wrote: post #18

jerf wrote: post #15

Earlier quoted context omitted.

"Where does all that 'entropy' come from?" Your scare quote suggests you may already know this, but for the benefit of others, the answer is that there isn't any. Fractals may look visually complicated, but their information content is fully captured by the routines used to generate them, which include the formula and the coloring system being used. This is one of the ways in which "information" is a highly counter-i…

Yes, that is what I mean. Why is there a disconnect between the complexity of the compact description and the naive description? Why are simple expressions not simple in all "natural" representations? This is not addressable with the contrived example of "you can create an encoding scheme that reduces an arbitrarily complex description to an arbitrarily short identifier". After all, this is not a constructed compress…

Post by andrewflnr » Mon, Sep 26, 2016, 7:34 PM UTC

Grue3 wrote: post #23

wyager wrote: post #19

Earlier quoted context omitted.

But computing machines aren't unpredictable. They are very predictable. They appear to pull complex structure out of the aether. Perhaps the interesting thing is that the set of n-bit programs expands to only 2^n possible outputs. Why are some finite number of infinite-length outputs accessible, but not others? Why does nature favor those sequences?

>But computing machines aren't unpredictable. They are very predictable. Are they though? A 5-state Turing machine might seem trivial, but there exist programs in it, that we don't know if they ever halt or not [1]. Their behavior is totally non-deterministic for our understanding. There are also minimalistic cellular automata that produce completely unpredictable patterns. [2] [1] https://en.wikipedia.org/wiki/Busy_…