Plotting

main.lua

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+--Bespoke script for calculating one-parameter family of real analytic solutions
+--to functional equation f'( f( x ) ) = x.
+
+--Idea: suppose f has fixed point 'p',
+--apply the chain rule to functional equation
+--get values of f's derivatives at p
+--get truncated taylor series expansion of f at p
+--plot to get some idea about values, convergence.
+
+
+local function PlotFunction( f )
+
+  local RESOLUTION = 1000
+
+  local points = {}
+  for n = 1, RESOLUTION do
+    points[ 2 * n - 1 ] = n / RESOLUTION
+    points[ 2 * n ] = f( n / RESOLUTION )
+  end
+
+  local tf = love.math.newTransform(
+      0, love.graphics.getHeight(),
+      0, love.graphics.getWidth(),
+      -love.graphics.getHeight())
+    
+  love.graphics.setColor( 1, 1, 1, 0.5 )
+  love.graphics.setLineWidth( 0.003 )
+  love.graphics.setLineJoin( "miter" )
+  love.graphics.setLineStyle( "smooth" )
+  local draw = love.draw or function() end
+
+  love.draw = function()
+    draw()
+    love.graphics.replaceTransform( tf )
+    love.graphics.line( points )
+  end
+
+  love.update = function( dt )
+    print( love.mouse.getPosition( ) )
+  end
+
+end
+
+PlotFunction( function( x ) return x * x end )
+PlotFunction( function( x ) return x * x * x end )
+PlotFunction( math.sin )
+PlotFunction( function( x ) return math.exp( x ) - 1 end )