readme

main.lua

@@ -1,7 +1,7 @@
 local enumerations = require 'enumerations'
 local twintree = require 'twintree'
 local step = coroutine.wrap( twintree.buildIncremental )
-local a = enumerations.NadFFI( 2 )
+local a = enumerations.Dyad()
 local b = enumerations.SternBrocot()
 step( a, b )
 
@@ -27,6 +27,7 @@ end
 
 local function paint()
   if not pointList then return end
+  numMapped = #pointList / 2
   local type = type
   --Make sure the whole point list consists of numbers!
   --We use the __call metamethod in non-number elements to coerce to numbers.
@@ -87,6 +88,7 @@ function love.update( dt )
   if love.keyboard.isScancodeDown "s" then repaint = true; cy = cy - dt * 0.1 / math.sqrt( zoomFactor ) end
   if love.keyboard.isScancodeDown "q" then repaint = true; zoom( 1 + dt ) end
   if love.keyboard.isScancodeDown "e" then repaint = true; zoom( 1 - dt ) end
+  if love.keyboard.isScancodeDown "space" then repaint = true; pointList = twintree.flat( twintree.build( 10000, a, b ) ) end
   if repaint then return paint() end
 end
 
@@ -95,9 +97,8 @@ function love.keypressed( key, code, isrepeat)
 end
 
 function love.load()
-  --pointList = twintree.flat( twintree.build( 10000, a, b ) )
+  pointList = twintree.flat( twintree.build( 10000, a, b ) )
-  --numMapped = #pointList / 2
+  numMapped = #pointList / 2
-  new()
   love.graphics.setPointSize( 3 )
   love.graphics.setLineWidth( 0.005 )
   paint()

readme.md

@@ -0,0 +1,15 @@
+This is a little LOVE script for plotting correspondences between dense countable ordered sets.
+To use: download LOVE2D, then run LOVE in the directory where this repo is saved.
+
+Any two countable dense total orders are order isomorphic.
+Using only this structure it is possible to explicitly construct an increasing bijection between these two orders.
+
+This implements the standard procedure for doing this in general, the "back-and-forth" method.
+Pass a function that generates an infinite sequence to the enumerator wrapper ( require 'enumeration' ),
+then pass the resulting enumerators to twintree.build ( require 'twintree' ).
+
+twintree.build takes a number as its first argument, and the pair of enumerators as its following two arguments.
+This number is the number of pairs of points in the support of the function (i.e., it's a partial function, only some large but finite number of points will be computed and plotted. The rest will be displayed by linear interpolation.).
+
+twintree.build returns two values, each is a binary tree.
+twintree.flat does a simultaneous inorder traversal of both trees, then interlaces the entries in a large, reused, 1-indexed Lua table that can be passed to love.graphics.line. Supposing the trees are traversed like { x_1, x_2, x_3, ... x_n } and { y_1, y_2, y_3, ..., y_n }, then the resulting table will be { x_1, y_1, x_2, y_2, x_3, y_3, ..., y_n }.