local function make_beat_wave(params)
	-- triangle wave - n results in the section above zero having width 1-n
	-- so triangle - (1-w) will give us width w
	-- time_wave_input is doubled and offset to put a peak on every beat.
	local triangle= {'triangle', {'+', .5, {'*', 2, params.time}}}
	local above_zero_is_width= {'-', triangle, {'-', 1, params.width}}
	-- height above zero needs to be 1, but is currently w.
	-- <result> / w will make the height 1
	local height_is_one= {'/', above_zero_is_width, params.width}
	-- then max is used to clip off the parts of the wave that are below
	-- zero, and we have a wave that is flat between peaks.
	local beat_wave= {'max', 0, height_is_one}
	local curved_wave= {'^', beat_wave, 2}
	return curved_wave
end

local function asymmetric_scaler(scale, time)
	return {'+', scale-1, {'*', scale, {'square', time}}}
end

local function shift_and_scale(thing, old_low, old_high, low, high)
	local old_size= old_high - old_low
	local new_size= high - low
	local scale_factor= new_size / old_size;
	return {'+', low, {'*', scale_factor, {'-', thing, old_low}}}
end

local custom_mods= {
	pound= {
		target= 'note_pos_x',
		equation= function(params, ops)
			local curved_wave= make_beat_wave{
				time= params.time,
				width= {'-', 1, make_beat_wave{time= params.time, width= .5}},
			}
			local inverter= {'square', {'+', .5, params.time}}
			local time_beat_factor= {'*', curved_wave, 20, inverter}
			-- On even beats, period will be 1 at the start of the animation,
			-- then go to 0 as the animation peaks.
			-- On odd beats, period will be 1 at the start, then go to 16 as the
			-- animation peaks.
			local period= {
				'-', 1,
				{'*', -1, asymmetric_scaler(17, {'+', .5, params.time}),
					make_beat_wave{time= params.time, width= .5},
				}
			}
			local note_beat_factor= check_op{
				ops.wave,
				{'+', params.wave_offset,
				 pi_div{'/',
								params.note_input,
								{'*', period, params.period},
				 },
				},
			}
			local time_and_beat= check_op{ops.factor, time_beat_factor, note_beat_factor}
			local equation= check_op{ops.level, params.level, time_and_beat}
			return equation
		end,
		params= {
			level= 1, note_input= 'y_offset', wave_offset= .5, period= 15,
			time= 'music_beat', width= .5,
		},
		ops= {
			level= '*', factor= '*', wave= 'sin',
		},
	},
}

local pound_params= {
	level= 4,
	-- slowing down time makes the animation visible.
	-- Applying a beat wave to the time slowdown makes it crazy.
	time= {mult= shift_and_scale(make_beat_wave{time= {'*', 'music_beat', .0625}, width= .5}, 0, 1, .25, 1)},
	note_input= {'^', 'y_offset', .75},
	wave_offset= {
		m= {'triangle', 'music_beat'},
		a= shift_and_scale(make_beat_wave{time= {'*', 'music_beat', .125}, width= .5}, 0, 1, -.5, 1.5)},
}

local mods= {
	columns= 4,
	{column= "all", start= 0, length= 256, 'pound', pound_params},
}

return mods, custom_mods