cool math functions v2

local folder = Instance.new("WorldModel",script)
local sc = 0

function swait(t)
    sc = sc + 1
    if sc >= t then
        sc = 0
        game:GetService("RunService").Heartbeat:Wait()
    end
end

function donut(s)
    local r = s/2
    local l = 100 + s*10
    local center = CFrame.new(0,s*2,-50)
    for i = 1,l do
        local x2 = r*math.cos(i*l/r)
        local y2 = r*math.sin(i*l/r)
        local scale = s/((s-s/4)-math.cos(2*i))
        local z2 = math.sin(x2-y2)+math.cos(x2+y2)+math.cos(x2/y2)
        local xy = CFrame.new(x2,y2,0)
        local part = Instance.new("Part")
        part.Color = Color3.fromHSV(math.abs(x2),255,255)
        part.Size = Vector3.new(1,1,1)
        part.CFrame = xy*center
        part.Anchored = true
        part.Parent = folder
    end
end

function infinity(s)
    game:GetService("RunService").Stepped:Connect(function(t)
        local center = CFrame.new(0,s*2,-50)
        local scale = s/((s-s/4)-math.cos(2*t))
        local x = scale*math.cos(t)
        local y = scale*math.sin(2*t)/2
        local z = scale*math.sin(2/t)*2
        local x2 = ((x+1)*s)
        local y2 = ((y-1)*s)
        local z2 = (x2+y2)
        local xy = CFrame.new(x2,y2,0)
        local part = Instance.new("Part")
        part.Material = Enum.Material.Neon
        part.Color = Color3.fromHSV(math.abs(x),255,255)
        part.Size = Vector3.new(1,1,1)
        part.CFrame = xy*center
        part.Anchored = true
        part.Parent = folder
    end)
end

function infinity2(s)
    local part = Instance.new("Part")
    part.Material = Enum.Material.Neon
    part.Size = Vector3.new(1,1,1)
    part.Anchored = true
    part.Parent = folder
    local att1,att2 = Instance.new("Attachment"),Instance.new("Attachment")
    att1.Position = Vector3.new(0,-0.5,0)
    att2.Position = Vector3.new(0,0.5,0)
    att1.Parent = part
    att2.Parent = part
    local trail = Instance.new("Trail")
    trail.Parent = part
    trail.Attachment0 = att1
    trail.Attachment1 = att2
    trail.FaceCamera = true
    trail.LightInfluence = 1
    trail.Transparency = NumberSequence.new(0,1)
    trail.MinLength = 0
    trail.Lifetime = 10
    game:GetService("RunService").Heartbeat:Connect(function(t)
        local center = CFrame.new(0,s*2,-50)
        local scale = s/((s-s/4)-math.cos(2*t))
        local x = scale*math.cos(t)
        local y = scale*math.sin(2*t)/2
        local z = scale*math.sin(2/t)*2
        local x2 = ((x+1)*s)
        local y2 = ((y-1)*s)
        local z2 = (x2+y2)
        local xy = CFrame.new(x2,y2,0)
        game:GetService("TweenService"):Create(part,TweenInfo.new(1),{CFrame = xy*center}):Play()
        trail.Color = ColorSequence.new(Color3.fromHSV(math.abs(x),255,255))
    end)
end

local sc = 0

function swait(t)
    sc = sc + 1
    if sc >= t then
        sc = 0
        game:GetService("RunService").Heartbeat:Wait()
    end
end

function mandelbrot(s)
    local width = s
    local height, wscale = width, 2/width
    local m, limit2 = 100, 16
    local iter = 0
    local center = CFrame.new(0,0,-50)
    local div = 10
    local size = width/height/div
    local i = 0

    local pf = Instance.new("Folder",script)
    local pt = {}

    local colors = {}

    for n = 1,m do
        local hu = math.sqrt(n/m)
        colors[n] = Color3.fromHSV(hu, 255, 150)
    end
    local function render()
        i = i + 1
        for y = 1,height do
            for x = 1,width do
                local a = x * wscale - 1.5
                local b = 2*y / height - 1

                local ca = a
                local cb = b

                local n = 0
                local sin = 1 -- math.sin(i/10)

                while (n < m) do
                    local aa = a * a - b * b
                    local bb = 2 * a * b
                    a = aa + ca * sin
                    b = bb + cb
                    if (a * a + b * b > limit2) then
                        break
                    end
                    n = n + 1
                end

                local bright = math.sqrt((n*limit2)%255)
                local color = colors[n]
                --color = Color3.new(bright,bright,bright)
                if (n == m) then
                    bright = 0
                    color = Color3.new()
                end
                local tp = ((y-1)*(width*1))+x
                local vs = Vector3.new(size,size,size*(bright*2))
                vs = Vector3.new(size,size,size)
                if 1 >= i then
                    local f = Instance.new('Part')
                    f.Material = Enum.Material.SmoothPlastic
                    f.Massless = true
                    f.Anchored = true
                    f.CanCollide = false
                    f.CastShadow = false
                    f.Color = color
                    f.Size = Vector3.new(1, 1, 1)
                    local mesh = Instance.new("BlockMesh")
                    mesh.Scale = vs
                    mesh.Parent = f
                    f.CFrame = center*CFrame.new(x*size,y*size,0)
                    f.Parent = pf
                    pt[tp] = f
                else
                    pt[tp].Color = color
                    if pt[tp]:FindFirstChildOfClass("BlockMesh") then
                        pt[tp]:FindFirstChildOfClass("BlockMesh").Scale = vs
                    end
                end
                swait(500)
            end
        end
    end
    spawn(function()
        while wait(0) do
            render()
        end
    end)
end

function tree(bl)
    local center = CFrame.new(0,bl/2,-50)
    local base = Instance.new("Part")
    base.Material = Enum.Material.SmoothPlastic
    base.Color = Color3.new(1,0,0)
    base.Size = Vector3.new()
    base.CFrame = center
    base.CastShadow = false
    base.Massless = true
    base.Anchored = true
    base.CanCollide = false
    base.Parent = folder
    local branches = {base}
    local function make_part(r)
        local p = base:Clone()
        p.Color = Color3.new(1-(r/bl),0,0)
        p.Parent = folder
        return p
    end
    local function connect(p1,p2,r)
        local a1 = Instance.new("Attachment",p1)
        local a2 = Instance.new("Attachment",p2)
        local bar = Instance.new("RodConstraint")
        bar.Attachment0 = a1
        bar.Attachment1 = a2
        bar.Color = BrickColor.new(Color3.new(1-(r/bl),0,0))
        bar.Parent = p1
        bar.Visible = true
    end
    local function extend(t, branch_length, shorten_by, angle, r)
        local new_length = 0
        local min_length = 5
        local div = 10
        if branch_length > min_length then
            local new = {}
            for i,v in pairs(t) do
                local up = make_part(r)
                up.CFrame = v.CFrame*CFrame.new(0,branch_length/div,0) -- up
                local left = make_part(r)
                left.CFrame = up.CFrame*CFrame.Angles(0,0,math.rad(angle))*CFrame.new(0,branch_length/div,0) -- left
                local right = make_part(r)
                right.CFrame = up.CFrame*CFrame.Angles(0,0,-math.rad(angle))*CFrame.new(0,branch_length/div,0) -- right
                connect(up,v,r)
                connect(left,up,r)
                connect(right,up,r)
                table.insert(new,1,left)
                table.insert(new,1,right)
                swait(100)
            end
            new_length = branch_length - shorten_by
            r = r + shorten_by
            extend(new, new_length, shorten_by, angle, r)
        end
    end
    extend(branches, bl, 5, 30, 1)
end

function pi(s)
    local Part0 = Instance.new("Part")
    local SurfaceGui1 = Instance.new("SurfaceGui")
    local TextLabel2 = Instance.new("TextBox")
    Part0.Parent = folder
    Part0.CFrame = CFrame.new(2.6149931, 8.83000565, -12.8999939, -1, 0, 0, 0, 1, 0, 0, 0, -1)
    Part0.Orientation = Vector3.new(0, 180, 0)
    Part0.Position = Vector3.new(2.6149931, 8.83000565, -20)
    Part0.Rotation = Vector3.new(-180, 0, -180)
    Part0.Color = Color3.new(0.0666667, 0.0666667, 0.0666667)
    Part0.Size = Vector3.new(19.2099972, 5.33999777, 2)
    Part0.Anchored = true
    Part0.BottomSurface = Enum.SurfaceType.Smooth
    Part0.BrickColor = BrickColor.new("Really black")
    Part0.CanCollide = false
    Part0.Material = Enum.Material.SmoothPlastic
    Part0.TopSurface = Enum.SurfaceType.Smooth
    Part0.brickColor = BrickColor.new("Really black")
    SurfaceGui1.Parent = Part0
    SurfaceGui1.CanvasSize = Vector2.new(400, 60)
    TextLabel2.Parent = SurfaceGui1
    TextLabel2.Size = UDim2.new(1, 0, 1, 0)
    TextLabel2.BackgroundColor = BrickColor.new("Institutional white")
    TextLabel2.BackgroundColor3 = Color3.new(1, 1, 1)
    TextLabel2.BackgroundTransparency = 1
    TextLabel2.BorderSizePixel = 0
    TextLabel2.Font = Enum.Font.SourceSansBold
    TextLabel2.FontSize = Enum.FontSize.Size36
    TextLabel2.Text = "Retreiving data.."
    TextLabel2.TextColor = BrickColor.new("Institutional white")
    TextLabel2.TextColor3 = Color3.new(1, 1, 1)
    TextLabel2.TextScaled = true
    TextLabel2.TextSize = 36
    TextLabel2.TextStrokeTransparency = 0
    TextLabel2.TextWrap = true
    TextLabel2.TextWrapped = true

    local text = TextLabel2

    wait()

    local n = 0
    local bs = s
    local start = 1
    local add = true
    game:GetService("RunService").Heartbeat:Connect(function()
        for i = start,s do
            i = (i*2)-1
            if add then
                n = n + 1/i
            else
                n = n - 1/i
            end
            add = not add
        end
        start = s
        s = s + bs
        text.Text = tostring(n*4) -- pi is 1/4 using this method
    end)
end

function triangle(s)
    local width = s
    local height = s
    local center = CFrame.new(0,0,-50)
    local div = 10
    local size = width/height/div
    local i = 0
    local pf = Instance.new("Folder",script)
    local pt = {}

    local function render()
        i = i + 1
        local m = {}
        m[math.floor(width/2)] = true
        for y = height, 1, -1 do
            local n = {}
            for x = 1, width do
                local color = Color3.new()
                if m[x] then
                    color = Color3.new(1,1,1)
                    n[x+1] = not n[x+1]
                    n[x-1] = not n[x-1]
                end
                local tp = ((y-1)*(width*1))+x
                if 1 >= i then
                    local f = Instance.new('Part')
                    f.Material = Enum.Material.SmoothPlastic
                    f.Massless = true
                    f.Anchored = true
                    f.CanCollide = false
                    f.CastShadow = false
                    f.Color = color
                    f.Size = Vector3.new(1, 1, 1)
                    local mesh = Instance.new("BlockMesh")
                    mesh.Scale = Vector3.new(size,size,size)
                    mesh.Parent = f
                    f.CFrame = center*CFrame.new(x*size,y*size,0)
                    f.Parent = pf
                    pt[tp] = f
                else
                    pt[tp].Color = color
                end
                swait(50)
            end
            m = n
        end
    end
    while true do
        render()
    end
end

local plr = owner -- sandbox value

plr.Chatted:Connect(function(msg)
    if msg:lower():sub(1,5) == 'inf2/' then
        local s = msg:sub(6)
        if tonumber(s) then
            infinity2(tonumber(s))
        end
    elseif msg:lower():sub(1,4) == 'inf/' then
        local s = msg:sub(5)
        if tonumber(s) then
            infinity(tonumber(s))
        end
    elseif msg:lower():sub(1,6) == 'donut/' then
        local s = msg:sub(7)
        if tonumber(s) then
            donut(tonumber(s))
        end
    elseif msg:lower():sub(1,5) == 'tree/' then
        local s = msg:sub(6)
        if tonumber(s) then
            tree(tonumber(s))
        end
    elseif msg:lower():sub(1,8) == 'fractal/' then
        local s = msg:sub(9)
        if tonumber(s) then
            mandelbrot(tonumber(s))
        end
    elseif msg:lower():sub(1,3) == 'pi/' then
        local s = msg:sub(4)
        if tonumber(s) then
            pi(tonumber(s))
        end
    elseif msg:lower():sub(1,9) == 'triangle/' then
        local s = msg:sub(10)
        if tonumber(s) then
            triangle(tonumber(s))
        end
    end
end)