How about integrating/summing values? Seems like if we interpret the Perlin noise values as "how much to change" instead of an absolute value we would get the e

How about integrating/summing values? Seems like if we interpret the Perlin noise values as "how much to change" instead of an absolute value we would get the end result immediately. However, it would be more difficult to determine a value just at a given point instead of walking first through all preceding points.