Upthorn

(feat. the golden ratio)

I've always been fond of:

for y = 0 to ScreenHeight
    for x = 0 to ScreenWidth
        if (((x - CenterX) ^ 2 + (y - CenterY) ^ 2) <= Radius ^ 2) then
            pset (x, y), fillColor
        end if
    next x
next y

It's got a little less overdraw, but it checks every pixel on the screen.

doneFlag = false
while (!doneFlag) 

	# reseed random so our new points aren't dependent on our old points
	random.seed()
	
	# get a random point on the screen
	x = random.randint(0, screenWidth)
	y = random.randint(0, screenHeight)
	
	# check if it's within the circle
	if (((x - CenterX)**2) + ((y - CenterY)**2)  <= r ** 2)
	
		# get a second random point on the screen
		x2 = random.randint(0, screenWidth)
		y2 = random.randint(0, screenHeight)
		
		# check if it's also within the circle
		if (((x2 - CenterX)**2) + ((y2 - CenterY)**2)  <= r ** 2)
			
			# draw a line between the points
			drawLine((x, y), (x2, y2), fillColor)
	
	# check if the circle has been filled
	doneFlag = true

	# iterate over every pixel on the screen
	for y = 0 to ScreenHeight
		for x = 0 to ScreenWidth

			# check if the pixel is part of the circle
			if (((x - CenterX) ** 2 + (y - CenterY) ** 2) <= r ** 2)

				# check if the pixel is the correct color
				if (getPix(x,y) != fillcolor)

					#if not, we aren't done
					doneFlag = false