Fruity Formula Controller generates automation control data based on userdefined formulae. It can be used for boolean (true or false) operations, like creating logic gates and conditional statements, where the output is dependent on the state of the variable(s). The Formula Controller will appear as a Formula ctrl  Out option in the Link dialog. It is just one of the many internal automation controllers available in FL Studio.
How to use:
Load Fruity Formula Controller in a Mixer FX Slot. NOTE: Renaming the Formula Controller will help you find the correct automation source when more than one is used in a project.
Enter a formula or select one from the plugin presets and make sure it compiles correctly.
Link the target Synth, Effect or FL Studio interface control to the 'Formula ctrl  Out' option (or custom name used at step 1) from the Link Dialog > 'Link assignment' menu.
Link other internal or external hardware controllers to variables A, B and C OR record A, B, C tweaks in realtime as the project is playing.
Alternatively, Fruity Formula Controller can be routed in Patcher.
Video Tutorials
Parameters
a/b/c  These knobs are the parameters, that can be used as variables in your formulas. Enter them into your formula as a, b and c variables (see the list of operators and functions below).
Formula  This is where you enter your formula. Press ENTER or Compile to compile a formula. If the formula is a valid mathematical expression, you will see a message 'Compiled ok' below the formula. If it's not, you will see a helpful error message. NOTE: The output of the formula must range between 0 to 1 in order to qualify as valid control data, values outside of that will be cut off. (see below).
?  Opens the Syntax, Objects and Functions table (see below).
Compile  Compiles the formula. Alternatively press ENTER when using the formula edit box.
Comments  Type comments here. If text exceeds the height of the window a scrollbar will appear on the right side. Supports RTF text from WordPad. The formula Monitor graph also displays behind the text for your convenience.
Monitor  Shows the output from the formula in realtime. NOTE: Many formulas will not display as a moving trace until you click Play on FL Studio's transport panel.
Syntax, Objects & Functions
The following syntax, functions and objects are supported by the Formula Controller:
Operators
Abbreviation
Description
Example
+
addition
a+b
*
multiplication
a*b

subtraction
ab
/
division
a/b
^
power
a^b
=
comparison, equal
a=b
in
same as =
a in b
<>
not equal
a=b
>
greater than
a>b
>=
greater than or equal
a>=b
<=
lesser than or equal
a<=b
<
lesser than
a<b
%
converts percentages into decimal values
Value%
!
factorial, returns the scalar part of a
a!*b
div
integer divide
Numerator div Denominator
mod
modulo, returns the remainder of a/b
a mod b
fmod
floating point modulo
a mod b
not
logical not, returns 1 when a <= 0.5 and 0 when a > 0.5
not a
or
logical or, returns 1 when a or b or both are > 0.5
a or b
and
logical and, returns 1 when both a and b are > 0.5
a and b
xor
logical xor, returns 1 when a or b is > 0.5
a xor b
shr
integer shift bits right (divide), equivalent to x/2^y
Value shr Amount
shl
integer shift bits left (multiply), equivalent to x*2^y
Value shl Amount
Functions
Abs
absolute, flips the negative part of an output into positive
Abs(a)
ArcCos
inverse cosine
ArcCos(a)
ArcCosh
hyperbolic inverse cosine
ArcCos(a)
ArcSin
inverse sine
ArcSin(a)
ArcTg
antitangent
ArcTg(a)
ArcTanh
hyperbolic inverse tangent
ArcTg(a)
ATan2
arctangent angle/quadrant of a given number
Atan2(a,b)
Case
returns b if a=1, else returns c
Case(a,b,c)
Cos
cosine
Cos(a)
Cosh
hyperbolic cosine
Cos(a)
CoSec
cosecant
CoSec(a)
DegToRad
convert degree value to radians
DegToRad(a)
Ceil
rounds up to nearest integer
Ceil(a)
Ctg
cotangent
Ctg(a)
Exp
exponential
Exp(a)
Floor
rounds down to nearest integer, same as Int
Floor(a)
Fold
wave folding operation
Fold(a)
Frac
fractional part
Frac(a)
GetTempo
returns current project tempo
GetTempo
If
if a > 0.5 then b, else c
if(a,b,c)
IfE
returns 1 if a=b
IfE(a,b)
IfG
returns 1 if a>b
IfG(a,b)
IfGE
returns 1 if a>=b
IfGE(a,b)
IfL
returns 1 if a<b
IfL(a,b)
IfLE
returns 1 if a<=b
IfLE(a,b)
Int
integral part
Int(a)
Inter
returns 1 if a > b and a < c. If c < b, b & c values will be swapped
Inter(a,b,c)
Internoswap
as Inter but doesn't swap a & b
Internoswap(a,b,c)
Intpower
integer power, Value^Power
Intpower(Value, Power)
Ln
logarithm base e
Ln(a)
Log10
logarithm base 10
Log10(a)
Log2
logarithm base 2
Log2(a)
LogN
logarithm a is the base, b is the number to calculate from
LogN(a,b)
Map
maps the value a into the range b..c, equivalent to x * (z  y) + y
Map(a,b,c)
Max
maximum, returns the greater input
Max(a,b)
Min
minimum, returns the lesser input
Min(a,b)
Neg
negative
Neg(a)
Pi
returns the value of pi
Pi
Power
floating point power, a^b
Power(a,b)
Pow
floating point power, a^b
Pow(a,b)
RadToDeg
convert radian value to degrees
RadToDeg(a)
Rand
outputs continuous random values (0..1)
Rand
Round
round to nearest integer
Round(a)
Sec
secant
Sec(a)
SeededRand
static random value (0..1), changes when seed is changed
SeededRand(Seed)
Sin
sine
Sin(a)
Sinh
hyperbolic sine
Sinh(a)
Sqrt
square root
Sqrt(a)
Sqr
square (same as a^2)
Sqr(a)
Sum
sum of arguments
Sum(a,b)
Tg
tangent
Tg(a)
Tan
tangent
Tan(a)
Tanh
hyperbolic tangent
Tanh(a)
Trunc
truncate, limits the number of digits right of the decimal point
Trunc(Value)
Warp
warps signal a around to warp point b
Warp(a,b)
Special (FL Studiorelated)
a
value of knob A
a
b
value of knob B
b
c
value of knob C
c
SongTime
song position, in quarters
SongTime()
Time
system time, in ms
Time()
Tension
Curves the line, positive or negtively depending on sign
Tension(Value,Rate of change)
Gadgets
Date
system date
Date()
MouseX
mouse cursor X position
MouseX()
MouseY
mouse cursor Y position
MouseY()
NOTE: Fruity Formula Controller is not case sensitive, so all of the operators, functions and variables will compile even if not typed in a similar manner as in this table.
Output
Fruity Formula Controller can only output values that are within the range of 0 to 1, values outside of this range will be calculated, but not visible in the Monitor view. For certain functions, there's a wider range of potential output
values outside of the visible range, which can be useful for intermediate steps of the calculation (i.e. before the final output value). For example, the CoSec() function by definition has a range of y≤−1 or y≥1, which means all real numbers except those
in between 1 and 1. In the image below, the CoSec() function has been resized (multiplied with a small number) to display a wider range in the output. There are also functions that only return integers, which means that without scaling they only appear to return either 1 or 0.
Manipulating Functions
Sine Function Example
Let's examine the formula 0.5*Sin(SongTime*Pi*2+0.25)+0.5, which outputs a sine wave. Below the formula has been broken down into individual components, described as A  amplitude multiplier, F  frequency multiplier, O  offset and P  phase offset.
Multiplication/division outside of the function (A) scales the amplitude of the output.
Multiplication/division inside of the function (F) scales the frequency of the output. A higher scalar value outputs a higher frequency.
Addition/subtraction outside of the function (O) offsets the output (moves it up or down).
Addition/subtraction inside of the function (P) offsets the starting phase of the output (moves it left or right).
To observe a moving trace, SongTime or Time must be used inside of the function, or alternatively any changing control data from outside of the Formula Controller connected to one of the variables.
Multiplying SongTime with a multiple of Pi makes the resulting waveform fit evenly into the length of a pattern. Pi represents half a cycle in radians, and 2*Pi represents a complete cycle. A sine wave is shaped symmetrically in every half cycle period. In order for the output to keep repeating a complete half cycle, the frequency must be scaled by a multiple of pi. Example: 0.5*Sin(SongTime*Pi*(Int(b*10))) + 0.5 creates a sine wave, where parameter b adjusts the frequency. The Int() function is used to transform b into integer values, so that the frequency can only be changed in half cycle increments (Pi * integer).
Example Formulas
Here is a collection of example formulas. If after copying and pasting into Fruity Formula Controller the output is stuck at 0, make sure parameters a, b and c are not all set to zero, and that you pressed Compile or ENTER key. Formulas that use SongTime will require Song/Pattern to be playing. Some results may at first look unexpected, depending on the positions of the parameters (adjust them and see what happens).
Basic Waveforms
Name
Description
Formula
Sine
basic sine wave
0.5*Sin(SongTime*Pi)+0.5
Sine
sine wave with an adjustable amplitude, frequency and offset
a*Sin(SongTime*Pi*b)+c
Sine
as above, but the frequency has discrete values
a*Sin(SongTime*Pi*(Int(b*10)))+c
Sine
sine wave with an adjustable amplitude, initial phase and offset
a*Sin(SongTime*Pi+b*Pi)+c
Triangle
basic triangle wave
0.319*ArcCos(Cos(SongTime*Pi))
Triangle
triangle wave with an adjustable amplitude, frequency and offset
a*ArcCos(Cos(SongTime*Pi*2*b))+c
Triangle
as above, but the frequency has discrete values
a*ArcCos(Cos(SongTime*Pi*(Int(b*10))))+c
Triangle
triangle with an adjustable amplitude, initial phase and offset
a*ArcCos(Cos(SongTime*Pi+b*Pi))+c
Sawtooth
basic sawtooth
Frac(SongTime)
Sawtooth
sawtooth with an adjustable amplitude, frequency and offset
a*Frac(SongTime*b*2)+c
Sawtooth
as above, but the frequency has discrete values
a*Frac(SongTime*0.5*Int(b*10))+c
Sawtooth
sawtooth with an adjustable direction
Abs(Round(a)Frac(SongTime))
Square
basic square with 50% duty cycle
Round(Frac(SongTime))
Square
basic square with 50% duty cycle (using a sine function)
Round(0.5*Sin(SongTime*Pi*2)+0.5)
Square
square with an adjustable amplitude, frequency and offset
a*Round(0.5*Sin(SongTime*Pi*2*b)+0.5)+c
Square
as above, but the frequency has discrete values
a*Round(0.5*Sin(SongTime*Pi*(Int(b*10)))+0.5)+c
Pulse
square with an adjustable pulse width
Round(0.5*Sin(SongTime*Pi)+a)
Pulse
square with an adjustable amplitude, frequency and pulse width
a*Round(Frac(SongTime*2*b)+0.5c)
Sample and hold
random output with adjustable amplitude, frequency and offset
b*SeededRand(Int(SongTime*a))+c
Miscellaneous
Distorted Sine
Slightly distorted sine with an adjustable frequency
Pi/5*ArcTg(Sin(SongTime*2*Pi*b))+0.5
Rectified Sine
Halfwave rectified sine with an adjustable frequency
Sin(SongTime*Pi*b)
Rectified Sine
Fullwave rectified sine with an adjustable amplitude and frequency
a*Abs(Sin(SongTime*Pi*b))
Cones
Nonlinear triangular shape with an adjustable amplitude, frequency and offset
Halfcircle like shape with an adjustable amplitude, frequency and offset
a*(0.5+0.5*Cos(SongTime*Pi*b+Pi))^(1/5)+c
Boolean Operations
Buffer
input equal to the output
a
NOT
inverse of buffer
1a
AND
both a and b must be 1 to return 1
a*b
OR
either a, b or both must be 1 to return 1
a+b
XOR
exclusive or, either a or b must be 1 to return 1
(a+b)=1
NAND
inverse of and
1(a*b)
NOR
inverse of or
(a+b)=0
XNOR
inverse of xor
a=b
NOTE: Boolean operations will behave correctly when using boolean values, either 1 or 0 (true or false). The operators used are regular arithmetic operators and may output different results with other types of values.
Plugin Credits: Didier Dambrin, Andrew Tumashinov
(RapidEvaluator)