enhanced ImageInTerminal support and UnicodePlots compatibility

README.md

@@ -24,7 +24,7 @@ The environment variable `JULIA_NUM_THREADS` can be used to enable the multi-thr
 
 Please share your favorite fractals as `Fatou` snippet in the [discussion thread](https://discourse.julialang.org/t/ann-fatou-jl-easily-share-julia-fractals)!
 
-## Basic Usage
+## PyPlot.jl compatability features
 
 The program can be initialized with `using Fatou, PyPlot` or `ImageInTerminal`.
 
@@ -88,6 +88,12 @@ basin(nf,2)
 
 ![D2(ϵ)](http://latex.codecogs.com/svg.latex?D_2(\epsilon)%20=%20\left\\{z\in\mathbb{C}:\left|\\,z%20-%20\frac{1}{\cos{\left%20(z%20\right%20)}}%20\left(1%20+%20i\right)%20\left(\sin{\left%20(z%20\right%20)}%20-%201\right)%20-%20\frac{\left(1%20+%20i\right)%20\left(\sin{\left%20(z%20-%20\frac{1}{\cos{\left%20(z%20\right%20)}}%20\left(1%20+%20i\right)%20\left(\sin{\left%20(z%20\right%20)}%20-%201\right)%20\right%20)}%20-%201\right)}{\cos{\left%20(z%20-%20\frac{1}{\cos{\left%20(z%20\right%20)}}%20\left(1%20+%20i\right)%20\left(\sin{\left%20(z%20\right%20)}%20-%201\right)%20\right%20)}}%20-%20r_i\\,\right|%3C\epsilon,\\,\forall%20r_i(\\,f(r_i)=0%20)\right\\})
 
+## ImageInTerminal.jl compatibility
+
+When `using ImageInTerminal`, the display of a `Fatou.FilledSet` will be plotted automatically in the terminal.
+The `orbit` method also has optional `UnicodePlots` compatibility.
+Additional plotting support can be added via Pull-Request by adding another `Requires` script to the `__init__()` function definition.
+
 ## Detailed Explanation
 
 View [Explore Fatou sets & Fractals](https://github.com/chakravala/Fatou.jl/wiki/Explore-Fatou-sets-&-fractals) in Wiki for detailed *examples*.

src/Fatou.jl

@@ -229,7 +229,7 @@ function newton(E;
 end
 
 # load additional functionality
-include("internals.jl")
+include("internals.jl"); include("orbitplot.jl")
 
 """
     basin(::Fatou.Define, ::Integer)
@@ -279,6 +279,7 @@ function __init__()
     println("Fatou detected $(Threads.nthreads()) julia threads.")
     @require PyPlot="d330b81b-6aea-500a-939a-2ce795aea3ee" include("pyplot.jl")
     @require ImageInTerminal="d8c32880-2388-543b-8c61-d9f865259254" include("term.jl")
+    @require UnicodePlots="b8865327-cd53-5732-bb35-84acbb429228" include("uniplots.jl")
 end
 
 end # module

src/orbitplot.jl

@@ -15,13 +15,12 @@ julia> juliafill("z^2-0.67",∂=[-1.25,1.5],x0=1.25,orbit=17,depth=3) |> orbit
 ```
 """
 function orbit(K::Define{FT,QT,CT}) where {FT,QT,CT}
+    !isdefined(Fatou,:UnicodePlots) && !isdefined(Fatou,:PyPlot) && throw(error("Requires `using PyPlot` or `using UnicodePlots`"))
     K.x0 == nothing ? (bi = K.∂[1:2]') : (bi = [K.∂[1:2]...,K.x0]')
     orbit(K.E,z->K.F(z,0),convert(Array{Float64},bi),K.orbit,K.depth,Int(K.n))
 end
 
-function orbit(E,f::Function,bi::Matrix{Float64},orb::Int=0,depth::Int=1,incr::Int=384; plt::Function=plot)
-    # prepare for next figure
-    figure()
+function real_orb(E,f::Function,bi::Matrix{Float64},orb::Int=0,depth::Int=1,incr::Int=384)
     # initalize array to depth
     N = zeros(incr,depth+1)
     bis = zeros(3)
@@ -34,8 +33,6 @@ function orbit(E,f::Function,bi::Matrix{Float64},orb::Int=0,depth::Int=1,incr::I
     for t ∈ 1:depth
         N[:,t+1] = broadcast(f,N[:,t])
     end
-    # plot background lines
-    plot(x[:],N[:,1],"k--",x[:],N[:,2])
     # initialize for orbit cobweb
     N2 = zeros(orb+1)
     N2[1] = bis[3];
@@ -53,29 +50,5 @@ function orbit(E,f::Function,bi::Matrix{Float64},orb::Int=0,depth::Int=1,incr::I
     orbit[1:3:siz,2] = N2[1:end-1]
     orbit[2:3:siz,2] = N2[2:end]
     orbit[3:3:siz,2] = N2[2:end]
-    # plot orbit cobweb path
-    plot(orbit[:,1],orbit[:,2],"r")
-    # plot f^2,f^3,f^4,...
-    for h ∈ 3:depth+1
-        plot(x,N[:,h],lw=1)
-    end
-    if ~(orb == 0)
-        plt(range(bi[1],stop=bi[2],length=length(N2)),N2[:],"gray",marker="x",linestyle=":",lw=1)
-        funs = [latexstring("\\phi(x_{0:$orb})")]
-        funt = ", IC: \$ x_0 = $(bis[3])\$, \$ n\\in0:$orb\$"
-    else
-        funs = []
-        funt = ""
-    end
-    # trim graph
-    d=1.07
-    xlim(bi[1],bi[2])
-    ylim(minimum([d*minimum(N[:,2]),0]),maximum([d*maximum(N[:,2]),0]))
-    # set title
-    fune = rdpm(Algebra.latex(E))
-    title(latexstring("\$ x \\mapsto $fune\$$funt"))
-    # set legend
-    legend(vcat([L"$y=x$",L"$\phi(x)$",L"(x_n,\phi(x_n))"],[latexstring("\\phi^{$x}(x)") for x ∈ 2:depth],funs))
-    tight_layout()
-    return
+    return x,N,N2,orbit,bis
 end

src/pyplot.jl

@@ -29,4 +29,35 @@ function plot(K::FilledSet;c::String="",bare::Bool=false)
     end
 end
 
-include("orbitplot.jl")
+function orbit(E,f::Function,bi::Matrix{Float64},orb::Int=0,depth::Int=1,incr::Int=384; plt::Function=plot)
+    x,N,N2,orbit,bis = real_orb(E,f,bi,orb,depth,incr)
+    # prepare for next figure
+    figure()
+    # plot background lines
+    plot(x[:],N[:,1],"k--",x[:],N[:,2])
+    # plot orbit cobweb path
+    plot(orbit[:,1],orbit[:,2],"r")
+    # plot f^2,f^3,f^4,...
+    for h ∈ 3:depth+1
+        plot(x,N[:,h],lw=1)
+    end
+    if ~(orb == 0)
+        plt(range(bi[1],stop=bi[2],length=length(N2)),N2[:],"gray",marker="x",linestyle=":",lw=1)
+        funs = [latexstring("\\phi(x_{0:$orb})")]
+        funt = ", IC: \$ x_0 = $(bis[3])\$, \$ n\\in0:$orb\$"
+    else
+        funs = []
+        funt = ""
+    end
+    # trim graph
+    d=1.07
+    xlim(bi[1],bi[2])
+    ylim(minimum([d*minimum(N[:,2]),0]),maximum([d*maximum(N[:,2]),0]))
+    # set title
+    fune = rdpm(Algebra.latex(E))
+    PyPlot.title(latexstring("\$ x \\mapsto $fune\$$funt"))
+    # set legend
+    legend(vcat([L"$y=x$",L"$\phi(x)$",L"(x_n,\phi(x_n))"],[latexstring("\\phi^{$x}(x)") for x ∈ 2:depth],funs))
+    tight_layout()
+    return
+end

src/term.jl

@@ -3,19 +3,22 @@
 
 using ImageInTerminal, ColorSchemes
 
+nonan(x) = isnan(x) ? 0.0 : x
+
 function Base.show(io::IO,K::FilledSet;c::String="",bare::Bool=false)
     # plot figure using imshow based in input preferences
     isempty(c) && (c = K.meta.cmap)
     S = size(K.iter)
     H = zeros(ColorSchemes.RGB{Float64},S...)
     C = getproperty(ColorSchemes, isempty(c) ? :balance : Symbol(c))
     if K.meta.iter
+        M = length(C)/(max(K.iter...)+2)
         for x ∈ 1:S[1], y ∈ 1:S[2]
-            H[x,y] = C[K.iter[x,y]]
+            H[x,y] = C[round(Int,M*K.iter[x,y]+1)]
         end
     else
         for x ∈ 1:S[1], y ∈ 1:S[2]
-            H[x,y] = get(C,K.mix[x,y])
+            H[x,y] = get(C,nonan(K.mix[x,y]))
         end
     end
     display(H)

src/uniplots.jl

@@ -0,0 +1,32 @@
+#   This file is part of Fatou.jl. It is licensed under the MIT license
+#   Copyright (C) 2019 Michael Reed
+
+using UnicodePlots
+
+function orbit(E,f::Function,bi::Matrix{Float64},orb::Int=0,depth::Int=1,incr::Int=384)
+    x,N,N2,orbit,bis = real_orb(E,f,bi,orb,depth,incr)
+    # trim graph
+    d=1.07
+    xl = bi[1:2]
+    yl = [minimum([d*minimum(N[:,2]),0]),maximum([d*maximum(N[:,2]),0])]
+    # plot background lines
+    plt = lineplot(x[:],N[:,1],xlim=xl,ylim=yl,color=:magenta,name="y=real(z)")
+    lineplot!(plt,x[:],N[:,2],color=:blue,name="ϕ(real(z))")
+    # plot orbit cobweb path
+    scatterplot!(plt,orbit[:,1],orbit[:,2],color=:red,name="(zₙ,ϕ(zₙ))")
+    # set legend
+    leg = ["ϕ^{$x}(z)" for x ∈ 2:depth]
+    # plot f^2,f^3,f^4,...
+    for h ∈ 3:depth+1
+        lineplot!(plt,x,N[:,h],color=isodd(h) ? :yellow : :green,name=leg[h-2])
+    end
+    if ~(orb == 0)
+        lineplot!(plt,collect(range(bi[1],stop=bi[2],length=length(N2))),N2[:],color=:cyan,name="ϕ(z_{0:$orb})")
+        funt = ", IC: z₀ = $(bis[3]), n∈0:$orb"
+    else
+        funt = ""
+    end
+    # set title
+    UnicodePlots.title!(plt,"z ↦ $E$funt")
+    return plt
+end