Decided to spruce up the Chaos modules for the library - here are 4 different versions for you to explore!
Chaos - Chaos modules are a special class of random modules used primarily for modulation. They are not purely random like white noise (where all values have an equal possibility of being chosen), and not “filtered” random like pink noise (where lower values have a greater chance of being chosen than higher values). Instead, chaos describes a system that is highly dependent on an initial state, and often contain feedback loops, where the previous state affects the next state. For example: in choosing random numbers, the previous number does not affect the probability of the value of the next number being chosen. A filtered random system can bias the set of numbers being chosen so that more low-value numbers are chosen (like with pink noise), but the previous number chosen still does not affect what number will be chosen next. Chaos on the other hand allows for previous values to influence future values that are chosen. Chaos modules make for interesting modulation sources as they tend to have a more organic or natural feel - almost as if a human hand or the wind were turning the knob. For more information and inspiration about chaos theory and mathematics, refer to this Wikipedia article.
1D Chaos Decay - Creates a one-dimensional chaos modulation and envelope decay source. The module begins with a modulation output of 0.5. Each time the module is clocked, a new value is chosen. The new value will be go halfway from its current position to 1 (0.75) or 0 (0.25). Each successive clock pulse will again choose halfway to 0 or halfway to 1. So if the current position after one clock pulse is 0.75, the next position could be halfway to 1 (0.875) or halfway to 0 (0.375). The bias knob tips the balance from a 50-50 chance to go up or down to 100% chance to go down (0) or 100% chance to go up (1). The slew knob eases transitions between each new value. The range knob offers 7 discrete ranges of slew limiting. Range value of 1 is the least amount of slew limiting, good for just barely taking the edge off of transitions, and a range value of 7 offers really long and slow transitions between each new value for when you want changes to happen over the course of several minutes. The range must be used in conjunction with the speed of the incoming clock. If the range is set to 7 with a fast incoming clock speed, the module will hover very closely to 0.5 without changing much ever. So as a general rule use slow clock speeds for higher slew range values. The decay control adjusts the speed of the decay of the 8 envelope outputs from 0.01 seconds to 30 seconds. The decay cycle is triggered whenever the value of the modulation output crosses each input.
1D Chaos Gate- Creates a one-dimensional chaos modulation amnd gate source. The module begins with a modulation output of 0.5. Each time the module is clocked, a new value is chosen. The new value will be go halfway from its current position to 1 (0.75) or 0 (0.25). Each successive clock pulse will again choose halfway to 0 or halfway to 1. So if the current position after one clock pulse is 0.75, the next position could be halfway to 1 (0.875) or halfway to 0 (0.375). The bias knob tips the balance from a 50-50 chance to go up or down to 100% chance to go down (0) or 100% chance to go up (1). The slew knob eases transitions between each new value. The range knob offers 7 discrete ranges of slew limiting. Range value of 1 is the least amount of slew limiting, good for just barely taking the edge off of transitions, and a range value of 7 offers really long and slow transitions between each new value for when you want changes to happen over the course of several minutes. The range must be used in conjunction with the speed of the incoming clock. If the range is set to 7 with a fast incoming clock speed, the module will hover very closely to 0.5 without changing much ever. So as a general rule use slow clock speeds for higher slew range values. The -/+ control is a positive domain attenuverter for the modulation output. The 8 gate outputs serve as both a meter and set of triggers for other modules.
2D Chaos Decay - Essentially the same as two 1D Chaos Decay modules, but with a 2D output matrix. Map the x and y outputs to dual parameters like delay time and feedback, left and right channel volume, or filter cutoff and resonance. Use the output gates to trigger chaotic events or step sequencers.
2D Chaos Gate - Essentially the same as two 1D Chaos Gate modules, but with a 2D output matrix. Map the x and y outputs to dual parameters like delay time and feedback, left and right channel volume, or filter cutoff and resonance. Use the output gates to trigger chaotic events or step sequencers.
@Stschoen - Thanks, but this is not the same as the 3d module actually! This is just a retooling of the chaos modules - in that 3d chaos patch the chaos module was driving one of the paramters on the 3d gate module.
@biminiroad - what are you using for your chaos source? I was considering building a double-pendulum model to create a 2D chaotic LFO, but maybe that's what you've already done.
@jjthrash - it's basically a die-rolling processing that chooses to go up or down based on white noise. I cribbed it from this video about Chaos. Instead of rolling a die, it's choosing a random number with a sample and hold and white noise, and there are just two points it's moving between rather than 3.
The important thing as far as I can tell in chaos is that the previous value affects what the next value can be. Like if it's 0.5, it will *only* be 0.75 or 0.25 on the next iteration. If it's 0.75, it can *only* be 0.875 or 0.375 on the next iteration.
@stschoen great patch! I literally still have not made my own demo patch with it, lol. I'm so burnt out, but I do have some cool ideas for this one, especially the decay one.
Actually I haven't yet used the primary output(s) on any of the chaos modules. The semi-random gates and decay have been interesting in their own right. I'm looking forward to experimenting with the primary chaotic outputs as well.