# Pkg.add("Decimals") # Not needed because this is on juliabox
using Plots
using Decimals

# Defining Variables
a = Decimal(0.15)
b = Decimal(0.2)
c = Decimal(1)
d = Decimal(-2)
n = Decimal(-0.5)
t = 0
cs =
phi = Decimal(0.5)
values = []
column = Dict()

# Creating the first column
while n < Decimal(0.5)
    column[string(n)] = a + b*n^1 + c*n^2 + d*n^3
    n = n + Decimal(0.02)
end

# Add the first column to the array of values
push!(values, column)

# Starting an infinite loop
while true
    n = Decimal(-0.5)
    column = Dict()

    # Creating the n'th column
    while n < Decimal(0.5)
        index = string(n)
        previousIndex = string(Decimal(n-Decimal(0.02)))
        if previousIndex == "-0.00"
            previousIndex = "0"
        end
        nextIndex = string((n+Decimal(0.02)))
        if index == "-0.5" || index == "0.5"
            column[index] = a + b*n^1 + c*n^2 + d*n^3
        else
            column[index] = Decimal(values[end][index] + (values[end][previousIndex]*phi - 2*values[end][index]*phi + values[end][nextIndex]*phi))
        end
        n = n+Decimal(0.02)
    end

    if length(values) > 1 && values[end-1] == values[end]
        break
    end

    push!(values, column)

    println(t)
#     println(values[end])

#     k = collect(keys(values[end]))
#     v = collect(values(values[end]))
#     plot(k, v)

    t = t + 4
end
println(values[1]["-0.48"])
println("done!")