First try at beeswarm - nothing actually works yet

src/beeswarm.jl

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+using Random: shuffle
+using Makie
+@recipe(Beeswarm, positions) do scene
+    return default_theme(scene, Scatter)
+end
+
+Makie.conversion_trait(::Type{<: Beeswarm}) = Makie.PointBased()
+
+function Makie.plot!(plot::Beeswarm)
+    positions = beeswarm.converted[1] # being PointBased, it should always receive a vector of Point2
+    markersize = beeswarm.markersize
+
+end
+
+function beeswarm_coords(olda, side = :both)
+
+    # what should be the new y position of a point given it's x and it's closest point
+    getypos(x, ptx, pty, cellsize) = pty + sqrt(cellsize^2-(ptx-x)^2)
+
+    # find the minimum y position for a given point
+    function minypos(xind, shift_signs = false)
+           neighbors = potential_interactions(xind)
+           length(neighbors) == 0 && return NaN
+           yvals, xvals = view(ys, neighbors), view(a, neighbors)
+           tmpyvals = shift_signs ? -yvals : yvals
+           limit = maximum(tmpyvals) - cellsize
+
+           ypos = zeros(length(xvals))
+           for i in eachindex(xvals)
+                  if tmpyvals[i] > limit
+                         ypos[i] = getypos(a[xind], xvals[i], tmpyvals[i], cellsize)
+                  end
+           end
+           ret = maximum(ypos) # Using maxmimum here is not an error - it is the closest point that determines the result
+           shift_signs ? -ret : ret
+    end
+
+    function update_ypos!(n_ypos, inds, shift_signs = false)
+           n_ypos[inds] .= minypos.(inds, shift_signs)
+    end
+
+    function potential_interactions(freeind)
+           outside_range(x) = abs(a[freeind]-a[x])>cellsize
+           lo_ind = findprev(outside_range, LinearIndices(a), freeind)
+           lo = isnothing(lo_ind) ? 1 : lo_ind + 1
+           hi_ind = findnext(outside_range, LinearIndices(a), freeind)
+           hi = isnothing(hi_ind) ? lastindex(a)-1 : hi_ind - 1
+           if lo != 0 && hi != 0 && hi >= lo
+                  included[freeind] ? (lo:hi)[.!(included[lo:hi])] : (lo:hi)[included[lo:hi]]
+           else
+                  Int[]
+           end
+    end
+
+    # estimate a pointsize
+    a = sort(shuffle(olda))
+    cellsize = (diff([extrema(a)...])/(length(a)^0.6))[1]
+
+    # vectors to hold return values
+    included, ys = falses(axes(a)), zeros(length(a))
+
+    # fill the first points, that are going to be along the middle line
+    ind = firstindex(a)
+    nearest_ypos = fill(NaN, length(a))
+    while !isnothing(ind)
+           included[ind] = true
+           ind = findfirst(v->v>a[ind] + cellsize, a)
+    end
+
+    # now fill the rest in turn
+    update_ypos!(nearest_ypos, findall(.!(included)))
+    innow = sum(included)
+
+    if side in (:left, :right)
+           while innow < length(a)
+                  newy, placenext = findmin(nearest_ypos)
+                  included[placenext] = true
+                  ys[placenext] = newy
+                  update_ypos!(nearest_ypos, potential_interactions(placenext))
+                  nearest_ypos[placenext] = NaN
+                  innow += 1
+           end
+    elseif side == :both
+           nearest_ypos_left = -copy(nearest_ypos)
+           nearest_ypos_right = nearest_ypos
+
+           while innow < length(a)
+                  newyleft, placenext_left = findmax(nearest_ypos_left)
+                  newyright, placenext_right = findmin(nearest_ypos_right)
+
+                  if -newyleft < newyright
+                         placenext = placenext_left
+                         included[placenext] = true
+                         ys[placenext] = newyleft
+                         update_ypos!(nearest_ypos_left, potential_interactions(placenext), true)
+                  else
+                         placenext = placenext_right
+                         included[placenext] = true
+                         ys[placenext] = newyright
+                         update_ypos!(nearest_ypos_right, potential_interactions(placenext))
+                  end
+
+                  nearest_ypos_right[placenext] = NaN
+                  nearest_ypos_left[placenext] = NaN
+                  innow += 1
+           end
+    else
+           error("side must be :left, :right, or :both")
+    end
+
+    @show ys
+
+    rety = zeros(length(olda))
+    rety[sortperm(olda)] .= ys
+
+    if side == :left
+           rety .*= -1
+    end
+    rety, olda
+end
+
+x,y = beeswarm_coords(collect(iris[!, :SepalLength]), :both)
+
+
+using DataFrames, RDatasets #, Plots
+iris = dataset("datasets", "iris")
+
+x,y = beeswarm_coords(collect(iris[!, :SepalLength]), :both)
+Makie.scatter(x,y, color = iris[!, :Species].refs, markersize = 7, axis = (; aspect = DataAspect()))