Code Doodles!

[Nixola]

There's a "maths" missing I fear

[slime]

The same thing happens on my school's computers (kinda old ) too - When I reduce the samples to 0 it works.

Apparently some Intel video drivers give back the Microsoft OpenGL 1.1 software renderer when an OpenGL context with 16x MSAA is requested.

I recommend using 8x MSAA at the most, and preferably 4x. There aren't many GPUs which support 16x MSAA, and as discovered by Nixola some drivers do unexpected things when you request it. The visual difference between 8x and 16x is very minimal anyway (and the performance difference can be large – when 16x is supported.)
Even 4x MSAA makes things look comparatively great, and it's the most-supported MSAA value across all GPUs.

[Garmelon]

There's a "maths" missing I fear

Fixed in the original post, just download it again

[HugoBDesigner]

I was bored, while at the same time curious about Pi. I decided to "study" it by seeing which digits are more common on it. You can try it yourself with different amounts of digits to consider, from 1 to 999:

Download main.lua

Or code itself (relatively big, thus the uploaded file):

Code: Select all

function love.load()
	pi = "3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420198"
	piMin, piMax = 1, string.len(pi)-2
	love.window.setTitle("A study of Pi")
	font1 = love.graphics.newFont(12)
	font2 = love.graphics.newFont(8)
	love.graphics.setFont(font1)
	love.window.setMode(400, 300)
	love.graphics.setLineWidth(2)
	
	keyHold = {t = 0, rt = 0, mt = 1, mrt = .02}
	
	counter = {0, 1, 0, 0, 0, 0, 0, 0, 0, 0}
	piDigits = 1
end

function love.update(dt)
	local down = love.keyboard.isDown
	local rp = 0
	if down("up") or down("=") or down("kp+") or down("right") then
		rp = 1
	elseif down("down") or down("-") or down("kp-") or down("left") then
		rp = -1
	else
		keyHold.t = 0
		keyHold.rt = 0
	end
	
	if rp ~= 0 then
		keyHold.t = math.min(keyHold.t + dt, keyHold.mt)
		if keyHold.t == keyHold.mt then
			keyHold.rt = keyHold.rt+dt
			if keyHold.rt >= keyHold.mrt then
				keyHold.rt = 0
				piDigits = math.min(piMax, math.max(piMin, piDigits+rp))
				updatePi()
			end
		end
	end
end

function love.draw()
	love.graphics.setFont(font1)
	local font = love.graphics.getFont()
	love.graphics.setColor(255, 255, 255, 255)
	love.graphics.print("Digits: " .. piDigits, 3, 3)
	
	local more, less = 1, 1
	for i, v in ipairs(counter) do
		if v/piDigits <= counter[less]/piDigits then
			less = i
		end
		if v/piDigits >= counter[more]/piDigits then
			more = i
		end
	end
	
	love.graphics.setColor(255, 255, 255, 55)
	for i = 1, 10 do
		love.graphics.rectangle("fill", 5, 100+(i-1)*5, 400-10, 1)
	end
	
	local t = {}
	for i = 1, #counter+2 do
		local l = i-1
		local n = 0
		if l >= 1 and l <= #counter then
			n = counter[l]/counter[more]
		end
		table.insert(t, n)
	end
	for i = 2, #t do
		local x1, x2 = math.max(5, (i-2)*(400/11)), math.min(400-5, (i-1)*(400/11))
		local y1, y2 = (100+9*5) - t[i-1]*(9*5), (100+9*5) - t[i]*(9*5)
		
		if i < #t then
			love.graphics.setColor(255, 255, 255, 55)
			love.graphics.setLineWidth(2)
			if i-1 == more then
				love.graphics.setColor(155, 155, 255, 105)
				love.graphics.setLineWidth(4)
			elseif i-1 == less then
				love.graphics.setColor(255, 155, 155, 105)
				love.graphics.setLineWidth(4)
			end
			love.graphics.line(x2, y2, x2, 100+9*5)
		end
		
		love.graphics.setLineWidth(2)
		love.graphics.setColor(0, 105, 255, 255)
		love.graphics.line(x1, y1, x2, y2)
	end
	
	love.graphics.setLineWidth(2)
	for i, v in ipairs(counter) do
		love.graphics.setColor(255, 255, 255, 255)
		local x = (400/11)*i
		
		love.graphics.print(i-1, x-font:getWidth(i-1)/2, 20)
		
		love.graphics.setColor(255, 255, 255, 255)
		if i == less then
			love.graphics.setColor(255, 155, 155, 255)
		elseif i == more then
			love.graphics.setColor(155, 155, 255, 255)
		end
		love.graphics.rectangle("line", x-5, 40, 10, 50)
		
		love.graphics.setColor(0, 255, 0, 255)
		love.graphics.rectangle("fill", x-4, 40+50-48*(v/piDigits), 8, 48*(v/piDigits))
	end
	
	love.graphics.setFont(font2)
	local font = love.graphics.getFont()
	
	local t = {""}
	for i = 1, string.len(pi) do
		local s = string.sub(pi, i, i)
		if font:getWidth(t[#t] .. s) >= 400-10 then
			table.insert(t, "")
		end
		t[#t] = t[#t] .. s
	end
	
	local w = 0
	for i, v in ipairs(t) do
		if string.len(v)+w >= piDigits+2 and w < piDigits+2 then
			local s = {"", ""}
			s[1] = string.sub(v, 1, piDigits+2-w)
			s[2] = string.sub(v, piDigits+3-w, -1)
			love.graphics.setColor(255, 205, 0, 255)
			love.graphics.print(s[1], 5, 300-5-(#t*10)+(i-1)*10)
			love.graphics.setColor(255, 205, 0, 105)
			love.graphics.print(s[2], 5+font:getWidth(s[1]), 300-5-(#t*10)+(i-1)*10)
		else
			love.graphics.setColor(255, 205, 0, 255)
			if string.len(v)+w >= piDigits+2 then
				love.graphics.setColor(255, 205, 0, 105)
			end
			love.graphics.print(v, 5, 300-5-(#t*10)+(i-1)*10)
		end
		w = w + string.len(v)
	end
end

function love.keypressed(key)
	if key == "up" or key == "=" or key == "kp+" or key == "right" then
		piDigits = math.min(piMax, piDigits+1)
		updatePi()
	elseif key == "down" or key == "-" or key == "kp-" or key == "left" then
		piDigits = math.max(piMin, piDigits-1)
		updatePi()
	end
end

function love.mousepressed(x, y, button)
	if button == "wu" then
		piDigits = math.min(piMax, piDigits+1)
		updatePi()
	elseif button == "wd" then
		piDigits = math.max(piMin, piDigits-1)
		updatePi()
	end
end

function updatePi()
	counter = {0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
	for i = 3, 2+piDigits do
		local d = tonumber(string.sub(pi, i, i))
		counter[d+1] = counter[d+1] + 1
	end
end

And a screenie, because why not?

[undef]

Ah, nice idea.

Edit: This is wrong:
Although I can tell you that pi is a transcendental number.
That means that every possible number sequence can be found in the post comma digits of pi, and therefore the numbers are evenly distributed.

[micha]

Ah, nice idea.
Although I can tell you that pi is a transcendental number.
That means that every possible number sequence can be found in the post comma digits of pi, and therefore the numbers are evenly distributed.

Sorry for the nit-picking, but this reasoning is not correct. You can make a transcendental number consisting only of the digits 0 and 1. Therefore not every possible number sequence appears in every transcendental number.

The statements (1) that every possible number can be found inside pi and (2) that the digits are evenly distributed in pi might still be true. I am not sure about that.

[DaedalusYoung]

The statements (1) that every possible number can be found inside pi and (2) that the digits are evenly distributed in pi might still be true. I am not sure about that.

There are an infinite number of digits, so every number will appear an infinite amount of times, so yeah, that should be true.

[micha]

There are an infinite number of digits, so every number will appear an infinite amount of times, so yeah, that should be true.

I know this is very off-topic, but this reasoning is again incorrect. We maybe know the first millions of digits of pi and we can see that all observed digits are approximately uniformly distributed. That is strong evidence but no proof that this pattern will continue indefinitely.

Further more, knowing that all numbers appear an infinite amount of times, does not mean that they all appear equally often.

But of course, there is good reason to believe that all the digits are uniformly distributed.

[zorg]

We do know that pi is transcendental, that only means that no rational a/b number equals it;
But according to wikipedia, we don't yet know whether pi is a Normal Number or not, meaning that the infinite digits in any base would be uniformly distributed or not.

[undef]

snip.

Sorry for the nit-picking, but this reasoning is not correct. You can make a transcendental number consisting only of the digits 0 and 1. Therefore not every possible number sequence appears in every transcendental number.

The statements (1) that every possible number can be found inside pi and (2) that the digits are evenly distributed in pi might still be true. I am not sure about that.

Oops sorry, my bad, I was wrong.
Learned something new again
(Would like someone to prove that pi is a normal number now...)