circle modular multiplication chord renderer

chord.rb

# with reference to rendered output but the OP
# https://www.reddit.com/r/mathpics/comments/3yzu77/heres_an_animated_version_of_that_circular/
# and a video guide
# https://www.youtube.com/watch?v=qhbuKbxJsk8

require "rmagick"

RESOLUTION = 800

def localToGlobalCoords(n)
	#local go from -1 to 1
	#global go from 0 to RESOLUTION
	#x always equals y, the image is square
	return ((n + 1)*(RESOLUTION/2)).floor
end
def ratioToX(n)
	return Math.cos(n*2*Math::PI)
end
def ratioToY(n)
	return Math.sin(n*2*Math::PI)
end
def ratioToCoords(n)
	return {x: ratioToX(n), y: ratioToY(n)}
end

def makeCircle(factor, modulo)
	#points = []
	#modulo.times do |index|
	#	points.push({number: index, x: ratioToX(index.to_f/modulo), y: ratioToY(index.to_f/modulo)})
	#end
	chords = []
	modulo.times do |index|
		chords.push({startPoint: ratioToCoords(index.to_f/modulo), endPoint: ratioToCoords(((factor*index.to_f)%modulo)/modulo)})
	end
	#return {points: points, chords: chords}
	return chords
end

def main
	currentModulo = 500
	(1..20000).each do |currentFactorInt|
		currentFactor = Rational(currentFactorInt, 100)
		circle = makeCircle(currentFactor, currentModulo)
		finalImage = Magick::Image.new(RESOLUTION, RESOLUTION) { self.background_color = "black" }
		draw = Magick::Draw.new
		draw.fill("white")
		draw.stroke("black")
		draw.circle(RESOLUTION/2, RESOLUTION/2, 0, RESOLUTION/2)
		currentHue = (currentFactorInt * 2) % 360
		circle.each do |currentChord|
			draw.stroke("hsb(#{currentHue.floor}, 255, 128)")
			currentHue += 0.2
			currentHue = currentHue % 360
			draw.line(localToGlobalCoords(currentChord[:startPoint][:x]), localToGlobalCoords(currentChord[:startPoint][:y]),
					  localToGlobalCoords(currentChord[:endPoint][:x]), localToGlobalCoords(currentChord[:endPoint][:y]))
		end
		draw.annotate(finalImage, 0, 0, 10, 10, "0 ≤ N ≤ #{currentModulo}") {
			self.font = "Droid-Sans-Mono"
			self.fill = "white" 
			self.stroke = "transparent" 
			self.pointsize = 20
			self.gravity = Magick::NorthEastGravity
		}
		draw.annotate(finalImage, 0, 0, 10, 10, "(#{currentFactor} * N) mod #{currentModulo}") {
			self.font = "Droid-Sans-Mono"
			self.fill = "white" 
			self.stroke = "transparent" 
			self.pointsize = 20
			self.gravity = Magick::SouthEastGravity
		}
		draw.draw(finalImage)
		finalImage.write("frames/%06d.png" % currentFactorInt)
		puts "wrote frame #{currentFactorInt}/#{20000}, factor #{currentFactor.to_s}"
	end
end

main()