How can I transition between random colors? [closed]

This is called interpolating (smoothly moving between two options).

We first generate both results, and then figure out how far in time we are between the two. If we're 80% through the transitioning time, we figure out a way to be 80% towards the second color.

The simplest way to interpolate is called linear interpolation. It's called linear since the rate is constant through the transition, so the graph of any of the values is a line.

If we use ROBLOX's Vector3s to store the colors, it becomes a little briefer to do the math, so that's what I'll do.

begin = Vector3.new(math.random(),math.random(),math.random())
finish = Vector3.new(math.random(),math.random(),math.random())

startTime = tick()
duration = 5 -- seconds

while tick() - startTime < duration do
    local progress = (tick() - startTime) / duration
    -- progress is now between 0 (completely `begin` color)
    -- and 1 (completely `end` color)
    local intermediate = finish * progress + ( 1 - progress ) * begin
    -- The above is just a "weighted average" of `finish` and `begin`
    local color = Color3.new(intermediate.x, intermediate.y, intermediate.z)
    -- Use color3 for whatever
    wait()
end

To make this loop, we just have to make a new finish but move finish into begin:

begin, finish = finish, Vector3.new(math.random(),math.random(),math.random())
-- follow the previous snippet,
-- then wrap the whole thing in a `while true do` loop