(a+1)y+b
recursions= y = (a + 1) × y + b, every 20 msA recursive generator: the last output times a + 1, plus b. Like the other y-equations it can cycle like an LFO or turn chaotic, depending on the inputs.
SEE IT MOVE
Computed in your browser with KINSPIRATION's FUN engine, step by step: this FUN keeps a state, so its output depends on what came before.
WHAT TO KNOW
INPUTS
a: the growth (negative values damp); b: the step.
OUTPUT RANGE
−1..+1, wrapping round from +1 to −1
USE IT FOR
A negative a settles at b / -a (a -0.5, b 0.5: 1); a positive a makes the output grow each step and wrap, irregular patterns that never settle (a 0.5, b 0.5).
WATCH OUT
A positive a never settles: each step is bigger than the last, the output wraps and can stick near one end. Keep a negative for a smooth approach to b / −a.
IN THE FACTORY PROGRAMS
No factory program uses it: one of the K2700's hidden tools.
HOW TO ON YOUR K2700 · 2046 Editor Template
The factory does not route (a+1)y+b to a sound on its own: set one up on 2046 Editor Template and hear it on the pitch.
In Program mode choose 2046 Editor Template, a plain one-layer program to build on (KEYPAD, 2046, ENTER).
Press EDIT, then MORE and DSP MOD. On the Pitch row set Source 1 to FUN2 and its Depth to 1200 ct: FUN2's result, −1 to +1, now bends the pitch up to an octave either way.
MORE, then LFO+. On the FUN2 row set Input a to -0.10 and Input b to 0.05.
Move to Function and turn the Alpha Wheel to (a+1)y+b.
Play a note: the pitch slides up 600 ct and stays, y = 0.9 × y + 0.05 settling at 0.5 in about half a second. A scoop made by a recursion.
Press EXIT and answer NO to leave the factory program as it was, or SAVE to keep your version on a USER ID.