The occurrence of twin primes does not follow an exponential pattern in relation to their position in the twin prime sequence. Instead, it is believed that twin primes become less frequent as numbers increase, following a distribution that can be described by the twin prime conjecture. This conjecture suggests that there are infinitely many twin primes, but does not imply that they appear at an exponential rate. Instead, the density of twin primes tends to decrease, and their distribution is more closely related to the general distribution of prime numbers rather than an exponential function.