One simple way would be to define colors at certain points in your range - as in your example, 0 is black, 65535 is purple, maybe 10000 is red, whatever you want to do. Set up a table with those key rgb values, and then simply interpolate between the rgb values of the key values above and below your input value to find the rgb color for any given value.
eg. if you're looking up the color for the value 1000, and your table has
value=0, color=(0,0,0)
value=5000, color=(255, 0, 255)
Then you would interpolate between these values to get the color (51, 0, 51)