Randomness versus an Algorithm with a Random Step (... one in the same?)

  I have spent the last two weeks trying to convince myself that an algorithm with a random step produces a different outcome than pure randomness does.  However, after much thought I am only partly satisfied with the explanation I have generated, and thus am seeking further clarification. In the most basic sense, to me randomness implies that any outcome can occur.  Think of a board (like a checkerboard) where a space may either be colored red or black.  If the coloring was random any pattern could emerge, it could be all black or red, it could be checkerboard, or it could have no distinguished pattern at all.  Every time you recolor (or if done on a program like mathematica you "refresh") the board you will have a different color configuration, whose result is independent of the last.  Now, just for comparisons sake let's use an algorithm to color the board.  Let's say no two colors can have direct, parallel contact, they can only touch on a diagonal.  Every time we recolor we will get the same, well known checkerboard, it will never change.  Lastly, let's use a random algorithm to color the board.  A computer algorithm for such a task would look something like (-1) codes for black (1) codes for red.  A table of size X, Y exists and the value of each space within this matrix is determined by (-1)^random integer.  If the random integer is even the value will be 1 so it will code for red and if the integer is odd the value will be -1 so it will code for black. It seems to me that the product of such an algorithm will be the same as in the first completely random board.  In fact the two results seem identical (right?).

The trouble that I ran into even with this simple analogy, is that in the random instance there are rules.  When thinking about how to randomly color the checkerboard, I didn't even stop to think about the steps involved.  You have to color each space (it can't be left without color) and the colors that you use must be red or black.  Is this in itself algorithmic?  Thus is the product of randomness really just anything? If the first instance was truly random maybe I would have ended up with a green space or a triangular space in stead of square spaces.  In an evolutionary sense would this translate into a rabbit producing an alligator offspring, or a tree growing upside down? (is this what true randomness is?)  If so, then yes, I agree there is a large diffence between randomenss and a random algorithm. Dennet, in this light I suppose I do  see your point evolution is not a random process, it is “algorithmic” with the random step of genetic inheritance.