stepsfrom

Stepsfrom is a term used in computer science and mathematics to denote the sequence of intermediate states produced when repeatedly applying a function starting from a given initial state. It is commonly used to describe how a system progresses in discrete steps from an initial condition to subsequent states.

Formally, if s0 is the initial state and f is a state-update function, the stepsfrom sequence is s0, s1, ..., sn where sk+1 = f(sk) for k from 0 to n-1. In dynamical systems this sequence is often referred to as the orbit of s0 under f.

In programming and data processing, stepsfrom can be used as a utility to generate intermediate states for debugging, simulations, animations, or time-series analyses. It is typically implemented as a function that returns a list or array containing the first n+1 states.

Example (pseudo-code):

function stepsfrom(s0, f, n) {

s = []

x = s0

for i from 0 to n:

s.append(x)

x = f(x)

return s

}

Variants and limitations: when f is non-deterministic or depends on external inputs, the sequence can branch or vary between runs. If the function yields infinitely many states, stepsfrom may be defined for a finite n or produced as a lazy sequence or streaming generator to avoid excessive memory usage.

See also: orbit, iteration, recurrence relation, trajectory.

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