👉 In mathematics, an automorphism is a function that permutes the elements of a set while preserving the order of the elements. An "autallylotriomorphic" transformation is one where each of its three components (the image, kernel and range) are also automorphic. A common example of an automorphism in this context is when you flip a coin 3 times. The first flip will result in heads with probability 1/2, tails with probability 1/2, and