In the first case shown, the total number of elements obtained doubles at every step; in the second case, it follows a Fibonacci sequence, and increases by a factor of roughly (1+Sqrt[5])/2 ≃ 1.618 at every step.

There is not a uniform correspondence between apparent sophistication of organisms and lengths of genetic programs: different species of amphibians, for example, have programs that can differ in length by a factor of a hundred, and can be as many as tens of billions of elements long.

But if the picture is enlarged by a factor of 3 or more then at normal reading distance it can become difficult to distinguish the textures—perhaps because the squares cover regions larger than the templates used at the lowest levels in our visual system.

The result of this is that any change in the initial position of a point will be amplified by a factor of two at each step.

Second, complex behavior inevitably involves many elaborate details, and since different ones of these details may happen to be the deciding factors in the fates of individual organisms, it becomes very difficult for natural selection to act in a consistent and definitive way.

And for the more general formulas shown on the previous page it may increase by a factor that is itself almost exponential at each step.

Conjunctive normal form (CNF) Or[…] ∧ Or[…] ∧ … is the rough analog of applying Factor .

Locally isotropic growth A convenient way to see what happens if elements of a surface grow isotropically is to divide the surface into a collection of very small circles, and then to expand the circle at each point by a factor h[x, y] .

History [of cryptography] Cryptography has been in use since antiquity, and has been a decisive factor in a remarkably large number of military and other campaigns. … Initially several different problems were considered, but after a while the only ones to survive were those such as the RSA system discussed below based essentially on the problem of factoring integers.

In the system x  Mod[2x, n] from page 257 , the repetition period MultiplicativeOrder[2, n] probably cannot always be computed in any polynomial of Log[n] steps, since otherwise FactorInteger[n] could also be computed in about this number of steps.