When the Voyager spacecraft took pictures of Saturn and Jupiter, they used Golay code to encode the data for transmission. Each 24-bit block of data could have up to three errors, and
the computers here on Earth could fix these errors. The Golay code is thus an error-correcting code. It was
originally published in 1949 with Marcel Golay's half-page paper, "Notes on Digital Coding." Today, this
paper is considered one of the most remarkable papers ever published, with deep, deep connections to group theory, graph theory, number theory, combinatorics, game theory, multidimensional geometry, and even
(slides a statement across)
Bank statements don't lie --
I have 511,108 dollars and 23 cents.
Tomorrow it'll be 511,114 dollars and
17 cents. Compounded daily. At our
preferred introductory rate.
You mentioned Fractal Analysis...?
Charlie holds her look, the fence-mending begins...
It came to me staring at a poster of
a drip painting on Emerson's wall...
how he sees the world -- whether in
an abstract painting, or a barcode,
or in the way he arranges seemingly
random clutter in his apartment --
-- it's all part of a larger design,
a fractal pattern...
...shapes repeating within the same
object -- like a snowflake.
Fractal curves can be generated from an initial
curve (often a regular polygon) and one or more replacement curves. Repeatedly, each line is replaced by a properly
scaled copy of one of the replacement curves. The buttons show the first iteration of the replacement curve used. The
fractal illustrated above is known as the Koch