particle simulator

local part = Instance.new("Part")
part.Size = Vector3.new(10,10,1)
part.Position = Vector3.new(0,10,20)
part.Anchored = true
part.CanCollide = false
part.Parent = script

local surface = Instance.new("SurfaceGui")
surface.SizingMode = Enum.SurfaceGuiSizingMode.PixelsPerStud
surface.PixelsPerStud = 50
surface.Parent = part

local main = Instance.new("Frame")
main.Size = UDim2.new(1,0,1,0)
main.BorderSizePixel = 0
main.BackgroundColor3 = Color3.new(0,0,0)
main.ClipsDescendants = true
main.Parent = surface

local particle_list = {}
local groups = {}
local particle_data = {}

local scale = 10 -- size and velocity scaling
local mas = main.AbsoluteSize

function create_particle(x,y)
    x = x or 0
    y = y or 0

    local p = Instance.new("Frame")
    p.Size = UDim2.new(0,scale,0,scale)
    p.Position = UDim2.new(0,mas.X/2,0,mas.Y/2)+UDim2.new(0,x*scale,0,y*scale)
    p.BackgroundColor3 = Color3.new(1,1,1)
    p.Name = #particle_list+1
    p.BorderSizePixel = 0
    p.Parent = main

    particle_data[p] = {}
    particle_data[p].force = Vector2.new(0,0)
    particle_data[p].position = Vector2.new(p.Position.X.Offset,p.Position.Y.Offset)
    particle_data[p].mass = 1

    table.insert(particle_list,p)
end

function update_divs(divs)
    for _,div in pairs(divs) do
        for x = 0,div do
            groups[div][x] = {}

            for y = 0,div do
                groups[div][x][y] = 0

                local visualize = false

                if visualize then
                    local p = Instance.new("Frame")
                    p.Size = UDim2.new(3,0,0,1)
                    p.Position = UDim2.new(0,mas.X/div*x,0,mas.Y/div*y)
                    p.BackgroundColor3 = Color3.new(1,1,1)
                    p.BackgroundTransparency = .9
                    p.BorderSizePixel = 0
                    p.Parent = main

                    local p = Instance.new("Frame")
                    p.Size = UDim2.new(0,1,3,0)
                    p.Position = UDim2.new(0,mas.X/div*x,0,mas.Y/div*y)
                    p.BackgroundColor3 = Color3.new(1,1,1)
                    p.BackgroundTransparency = .9
                    p.BorderSizePixel = 0
                    p.Parent = main
                end
            end
        end
    end
    for i,v in ipairs(particle_list) do -- first establish group population
        local pos = v.Position
        for _,div in pairs(divs) do
            local x = math.floor(pos.X.Offset/mas.X*div)
            local y = math.floor(pos.Y.Offset/mas.Y*div)

            if div > x and div > y and x > 0 and y > 0 then
                groups[div][x][y] += 1 -- increase population in group area
            end
        end
    end
end

function update_groups()
    local divs = {60,40,20}
    local total_div = 0

    for _,div in pairs(divs) do
        total_div += div
        groups[div] = {}
    end
    update_divs(divs)

    for i,v in ipairs(particle_list) do -- update colors
        local pos = v.Position

        local pop = 0

        for _,div in pairs(divs) do
            local x = math.floor(pos.X.Offset/mas.X*div)
            local y = math.floor(pos.Y.Offset/mas.Y*div)

            if div > x and div > y and x > 0 and y > 0 then
                local divpop = groups[div][x][y]
                pop += divpop^2/(mas.X/div)
            end
        end

        local radiance = pop
        v.BackgroundColor3 = Color3.new(radiance,radiance,radiance)
        --v.BackgroundColor3 = Color3.new(0.4+radiance*0.4,0.8-radiance*0.4,0.8-radiance*0.4)
    end

    --[[ -- supposed to update gravity with large amounts of particles but im lazy to add
    for _,p in ipairs(particle_list) do -- update gravity
        local pos = p.Position

        local force = 0

        for _,div in pairs(divs) do
            local x = math.floor(pos.X.Offset/mas.X*div)
            local y = math.floor(pos.Y.Offset/mas.Y*div)

            if div > x and div > y and x > 0 and y > 0 then
                local divpop = groups[div][x][y]
                force += divpop/(mas.X/div) -- all the particles have mass of 1, no extra steps
            end
        end

        local p_vec = Vector2.new(p.Position.X.Offset,p.Position.Y.Offset)
        local new_vec = p_vec+force

        p.Position = UDim2.new(0,new_vec.X,0,new_vec.Y)
    end
    ]]
end

function update_particle(p)
    local G = 6.67408 * 10^-4--1/1000
    for i,v in ipairs(particle_list) do
        if v ~= p then
            local m1 = particle_data[p].mass
            local m2 = particle_data[v].mass
            local p_vec = particle_data[p].position
            local v_vec = particle_data[v].position
            local force_vec = v_vec-p_vec
            local r = force_vec.Magnitude
            local F = G*(m1*m2)/r^2
            local A = F/m1
            if r > 0 then
                force_vec = force_vec*A
            end
            force_vec = particle_data[p].force+force_vec
            particle_data[p].force = force_vec

            local new_vec = p_vec+force_vec
            particle_data[p].position = new_vec
            --p.Position = UDim2.new(0,new_vec.X,0,new_vec.Y)
        end
    end
end

function update_sim()
    for _,p in ipairs(particle_list) do
        update_particle(p)
    end
    for _,p in ipairs(particle_list) do
        local new_vec = particle_data[p].position
        p.Position = UDim2.new(0,new_vec.X,0,new_vec.Y)
    end
    update_groups()
end

local mx = 10
local my = 10

for x = 1,mx do
    for y = 1,my do
        create_particle((-mx*2/2)+x*2,(-my*2/2)+y*2)
    end
end

update_groups()

task.wait(3)

while true do
    update_sim()
    task.wait()
end