The number of different possible icons is an enormous number,
comprising more than seventy million digits. However, we do know that
the number ends in a four (because 128 x 128 equals 16384, and if you
multiply any number ending in 4 by itself an even number of times the
answer will also end in 4).
Here's another way to think of just how big this number is:
Suppose every person in the world produced one million icons every
second, and had been doing this for the entire estimated history of
the universe (say 20 billion years). The number of icons produced
would be then less than ten to the power 31. That's not even one
billionth of one percent of the possible icons. In fact it doesn't
even scratch the surface of the journey towards one billionth of one
percent of the possible icons.
Let's look at it another way. If you were to write this number down,
at 10 digits per inch, you would need a piece of paper more than a
hundred miles long to contain it.
The number of particles in the universe is well below one googol (a
number with 101 digits), yet the number of different icons is a number
with more than seventy million digits!
Incidentally, I get 70,380,813 digits whereas kottekoe-ga gets
70,706,234. I'm pretty sure that's because Google's calculator is
using logarithms internally when it evaluates 14*(2^24) and therefore
generating additional rounding error. If I type the following into
14 * 16700000 * (log 2)
then I get 70,380,813. This agrees with the KCalc calculator, which
gives an approximate answer of 9.68810425007 times ten to the
70,380,812 when I enter the expression (128*128)^16,700,000.
I trust you find this information interesting and useful for your work of art.
You may also be interested in the following question by ioawnat-ga,
who is printing every possible version of a book and is seeking a
universe big enough to hold a box that will contain them all:
"Google Answers - Large Number Computation"
Request for Answer Clarification by
14 May 2006 09:50 PDT
Thank you all so much for your enthusiastic contributions. Can I
clarify one thing... Is the number 2^24 (16,777,216) the same as 32
Lastly, if any of you would like to be added to the credits for this
work of art, please email me with your names:
chris (at) fallt (dot) com
Clarification of Answer by
14 May 2006 12:35 PDT
When a graphics format has "32 bits per pixel", it generally contains
8 bits of information for each primary colour - red, green, blue. This
gives 24 bits per pixel of colour information. The remaining eight
bits per pixel may be unused, or they may be used for some other kind
of information (typically for transparency data).
Therefore, each pixel within your icon has one out of 2^24
(16,777,216) possible colours. If all 32 bits carried colour
information, there would instead be 2^32 (4,294,967,296) possible
colours for each pixel.
Thanks for the kind offer of credit - you may credit my work as
"eiffel-ga (Google Answers Researcher)".