#!/usr/bin/env julia

# Jacek Poziemski 272389

import Pkg
Pkg.add("Plots")
using Plots

"""
    seq(x::Float64, c::Float64)::Float64

Calculate `x^2 + c`.

# Arguments
- `x::Float64`: the first argument
- `c::Float64`: the second argument
"""
function seq(x::Float64, c::Float64)::Float64
    return x^2 + c
end

cs::Vector{Float64} = [-2.0, -2.0, -2.0, -1.0, -1.0, -1.0, -1.0]
xs::Vector{Float64} = [1.0, 2.0, 1.99999999999999, 1.0, -1.0, 0.75, 0.25]

"""
    exp(x::Float64, c::Float64)::Vector{Float64}

Iterate over the seq function 40 times.

# Arguments
- `x::Float64`: the first argument
- `c::Float64`: the second argument
"""
function exp(x::Float64, c::Float64)::Vector{Float64}
    ret::Vector{Float64} = []
    push!(ret, x)

    for i in 1:40
        x = seq(x, c)
        push!(ret, x)
    end

    return ret
end

sequences::Vector{Vector{Float64}} = []

for i in 1:7
    sequence::Vector{Float64} = exp(xs[i], cs[i])
    push!(sequences, sequence)
end

for i in 1:length(sequences)
    plot(title = "x_n² + c", xlabel = "n", ylabel = "x_n")
    plot!(0:40, sequences[i], label = "x = $(xs[i]), c = $(cs[i])", lw = 2)
    png("6.$i.png")
end