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Random numbers play a key role in diverse fields of cryptography, stochastic simulations, gaming, etc. Random numbers used in cryptography must satisfy additional properties of forward secrecy. Chaotic systems have been a potential source of random number generators. Both lower (One-dimension) and higher (two, three-dimension) chaotic systems are popularized in the generation of random bit sequences. Higher-order chaotic systems have a higher resistance to attacks owing to multiple dimensional outputs. Logistic map initially designed in one-dimension has been extended to two- dimensions to improve security. This paper proposes to use the concept of biological Gene Dominance to further improvise the randomness of 2D Logistic map. The sequences X and Y are considered to be parent genes that determine the value of parameter ‘r’ for the next iteration. The scatter plot of the proposed 2D …