Lists

A list in square brackets behaves as one value: arithmetic on it applies element by element, and a function of a list returns a list.

examples/08-lists.axis

"Lists"

N = [1, 2, 3, 4, 5, 6, 7, 8] @ hidden

folder "Building lists" {
    "Arithmetic maps over every element."
    squares = N ^ 2 @ hidden
    "join glues lists together, sort orders them."
    both = join(N, squares) @ hidden
    ordered = sort(both) @ hidden
    "repeat builds a list of one repeated value."
    flat = repeat(3, 5) @ hidden
    "L[3] indexes, length counts."
    third = ordered[3] @ hidden
    size = length(ordered) @ hidden
    "An index takes a range, and may leave an end off: from the fourth on, the first three."
    rest = ordered[4...] @ hidden
    first = ordered[...3] @ hidden
}

folder "Lists as points" {
    "Two lists paired coordinate-wise become a list of points."
    (N, N ^ 2) @ color: RED, pointSize: 12
    "One list against a function of it."
    (N, sqrt(N)) @ color: BLUE, pointSize: 12
    "lines connects them into a path, and points: false leaves only that."
    (N, 0.5N) @ color: GREEN, lines, points: false, lineWidth: 3
}

folder "A list of graphs" {
    "A list where a constant would go draws one curve per element."
    K = [-3, -2, -1, 0, 1, 2, 3] @ hidden
    y = x + K @ color: PURPLE, lineOpacity: 0.6
    "The same trick on a family of circles."
    R = [1, 2, 3, 4] @ hidden
    x ^ 2 + y ^ 2 = R ^ 2 @ color: ORANGE, lineOpacity: 0.7
}

folder "Lists built from a rule" {
    "[1...10] is the range; `for` runs an expression over it."
    S = [i ^ 2 for i = [1...10]] @ hidden
    "The comprehension is a list like any other."
    (S, sqrt(S)) @ color: RED, pointSize: 12
    "Two variables after `for` pair off every combination."
    G = [(a, b) for a = [-4...4], b = [1, 2]] @ color: BLUE, pointSize: 8, lines: false
    "random() draws a number in [0, 1); random(n) draws a list of n."
    seed = random() @ hidden
    noise = random(length(N)) @ hidden
    (N, noise) @ color: GREEN, pointSize: 12, lines: false
}

Open in playground →