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A NumberSequence represents a series of number values from 0 to 1. The number values are expressed using the datatype/NumberSequenceKeypoint type. This type is used in properties of ParticleEmitter to indicate properties of particles over their lifetime. In Studio, this data type is edited using a line graph:

A NumberSequence for a ParticleEmitter's Transparency

The above line graph can be set using a script using the following call to

particleEmitter.Transparency ={, 0), -- (time, value), .75),, 1)


Two NumberSequences are equivalent if and only if the values of their datatype/NumberSequenceKeypoint are equivalent, even if the two NumberSequence would result in similar graphs.


The NumberSequence type does not have a built-in method for getting the value at a certain time/point because keypoints can have random envelopes. Assuming the envelope values of your keypoints are all 0, you can use the following function to evaluate at a specific time:

function evalNS(ns, time)
	-- If we are at 0 or 1, return the first or last value respectively
	if time == 0 then return ns.Keypoints[1].Value end
	if time == 1 then return ns.Keypoints[#ns.Keypoints].Value end
	-- Step through each sequential pair of keypoints and see if alpha
	-- lies between the points' time values.
	for i = 1, #ns.Keypoints - 1 do
		local this = ns.Keypoints[i]
		local next = ns.Keypoints[i + 1]
		if time >= this.Time and time < next.Time then
			-- Calculate how far alpha lies between the points
			local alpha = (time - this.Time) / (next.Time - this.Time)
			-- Evaluate the real value between the points using alpha
			return (next.Value - this.Value) * alpha + this.Value

You can use the function above like this:

local ns ={, 0),, .8),, 1),

print(evalNS(ns, 0))   --> 0
print(evalNS(ns, .25)) --> .4
print(evalNS(ns, .5))  --> .8
print(evalNS(ns, .75)) --> .9
print(evalNS(ns, 1))   --> 1