In white noise, there is no correlation in between successive frequencies.
To be white is to be colorless. White noise is a colorless hiss that is just as dull whether you play it faster or slower. It's autocorrelation function, which measures how its fluctuations at any moment are related to previous fluctations is zero.
Brown noise
Brown noise gets its name from the random walks of physical Brownian motion.
Each frequency is a random deviation of the previous frequency.
Pink noise
While white noise has no correlation between successive frequncies and brown noise has a very strong correlation, pink noise lies between.
Pink noise is sometimes referred to as 1/f noise (Voss & Clarke, 1978).
Gardner described 1978 a method to approximate pink noise. The method was invented by Voss.