strange_attractor.py

from europi import *
import machine
from europi_script import EuroPiScript
from utime import ticks_diff, ticks_ms
from math import fabs, floor
from random import choice

"""
Strange Attractor
author: Sean Bechhofer (github.com/seanbechhofer)
date: 2022-03-15
labels: gates, triggers, randomness

Strange Attractor is a source of chaotic modulation. It can use a variety of different implementations.

Outputs 1, 2 and 3 are based on the x, y and z values generated by the attractor.

Outputs 4, 5 and 6 are gates based on the values of x, y and z and relationships between them.

digital_in: Pause motion when HIGH
analog_in:

knob_1: Adjust speed
knob_2: Adjust threshold for triggers

button_1: Decrease output voltage range, change equation system
button_2: Increase output voltage range

output_1: x
output_2: y
output_3: z
output_4: triggers/gates
output_5: triggers/gates
output_6: triggers/gates

"""
# Version number

VERSION = "1.0"

# Maximum voltage output. Cranking this up may cause issues with some modules.
MAX_OUTPUT = MAX_OUTPUT_VOLTAGE

"""
Implementation of strange attractors, providing chaotic values for modulation.

* Lorenz. Well known system of equations giving chaotic behaviour.
  See https://en.wikipedia.org/wiki/Lorenz_system
* Pan-Xu-Zhou.
  See https://www.semanticscholar.org/paper/Controlling-a-Novel-Chaotic-Attractor-using-Linear-Pan-Xu/72f9c1b1f892b3aeea26af330d44011a20250f32
* Rikitake. Used to model the earth's geomagnetic field and explain the irregular switch in polarity.
  See Llibre, Jaume & Messias, Marcelo. (2009). Global dynamics of the Rikitake system. Physica D: Nonlinear Phenomena. 238. 241-252. 10.1016/j.physd.2008.10.011.
* Rossler. Use with caution. The z co-ord sits around zero for long periods.
  See https://en.wikipedia.org/wiki/R%C3%B6ssler_attractor
"""


class Attractor:
    def __init__(self, point=(0.0, 1.0, 1.05), dt=0.01, name="Attractor"):
        self.initial_state = point
        self.x = point[0]
        self.y = point[1]
        self.z = point[2]
        self.dt = dt
        self.name = name
        self.x_min = self.x
        self.y_min = self.y
        self.z_min = self.z
        self.x_max = self.x
        self.y_max = self.y
        self.z_max = self.z
        # arbitrary initial range values
        self.x_range = 100
        self.y_range = 100
        self.z_range = 100

    # The range of values produced depends on the parameters and the
    # specifics of the equations. If we know the range, we can then
    # normalise coordinates for use when generating CV. This method
    # runs through a number of iterations to estimate ranges.
    def estimate_ranges(self, steps=100000):

        # Execute a number of steps to get upper and lower bounds.
        for i in range(steps):
            self.step()

            self.x_max = max(self.x, self.x_max)
            self.y_max = max(self.y, self.y_max)
            self.z_max = max(self.z, self.z_max)
            self.x_min = min(self.x, self.x_min)
            self.y_min = min(self.y, self.y_min)
            self.z_min = min(self.z, self.z_min)

        self.set_range(self.x_min, self.x_max, self.y_min, self.y_max, self.z_min, self.z_max)

        # Reset to initial parameters
        self.x = self.initial_state[0]
        self.y = self.initial_state[1]
        self.z = self.initial_state[2]

    def set_range(self, x_min, x_max, y_min, y_max, z_min, z_max):
        self.x_max = x_max
        self.y_max = y_max
        self.z_max = z_max
        self.x_min = x_min
        self.y_min = y_min
        self.z_min = z_min

        self.x_range = self.x_max - self.x_min
        self.y_range = self.y_max - self.y_min
        self.z_range = self.z_max - self.z_min

    def x_scaled(self):
        return (100.0 * (self.x - self.x_min)) / self.x_range

    def y_scaled(self):
        return (100.0 * (self.y - self.y_min)) / self.y_range

    def z_scaled(self):
        return (100.0 * (self.z - self.z_min)) / self.z_range

    def __str__(self):
        return f"{self.name:>16} ({self.x:2.2f},{self.y:2.2f},{self.z:2.2f})({self.x_scaled():2.2f},{self.y_scaled():2.2f},{self.z_scaled():2.2f})"

    def step(self):
        """
        Update the point. This needs to be implemented in subclasses.
        """
        pass


"""
Implementation of a simple Lorenz Attractor, see

https://en.wikipedia.org/wiki/Lorenz_system

Default uses well known values of s=10,r=28,b=2.667.
"""


class Lorenz(Attractor):
    def __init__(self, point=(0.0, 1.0, 1.05), params=(10, 28, 2.667), dt=0.01):
        super().__init__(point, dt, "Lorenz")
        self.s = params[0]
        self.r = params[1]
        self.b = params[2]

    def step(self):
        """
        Update the point.
        """
        x_dot = self.s * (self.y - self.x)
        y_dot = self.r * self.x - self.y - self.x * self.z
        z_dot = self.x * self.y - self.b * self.z
        self.x += x_dot * self.dt
        self.y += y_dot * self.dt
        self.z += z_dot * self.dt


# Pan-Xu-Zhou
"""
Implementation of Pan-Xu-Zhou
"""


class PanXuZhou(Attractor):
    def __init__(self, point=(1.0, 1.0, 1.0), params=(10.0, 2.667, 16.0), dt=0.01):
        super().__init__(point, dt, "Pan-Xu-Zhou")
        self.a = params[0]
        self.b = params[1]
        self.c = params[2]

    def step(self):
        """
        Update the point.
        """
        x_dot = self.a * (self.y - self.x)
        y_dot = self.c * self.x - self.x * self.z
        z_dot = self.x * self.y - self.b * self.z
        self.x += x_dot * self.dt
        self.y += y_dot * self.dt
        self.z += z_dot * self.dt


"""
Implementation of Rossler. The z co-rd spends a lot of time around zero, so use with caution.
"""


class Rossler(Attractor):
    def __init__(self, point=(0.1, 0.0, -0.1), params=(0.13, 0.2, 6.5), dt=0.01):
        super().__init__(point, dt, "Rossler")
        self.a = params[0]
        self.b = params[1]
        self.c = params[2]

    def step(self):
        """
        Update the point.
        """
        x_dot = -(self.y + self.z)
        y_dot = self.x + self.a * self.y
        z_dot = self.b + self.z * (self.x - self.c)
        self.x += x_dot * self.dt
        self.y += y_dot * self.dt
        self.z += z_dot * self.dt


"""
Implementation of Rikitake.
"""


class Rikitake(Attractor):
    def __init__(self, point=(0.1, 0.0, -0.1), params=(5.0, 2.0), dt=0.01):
        super().__init__(point, dt, "Rikitake")
        self.a = params[0]
        self.mu = params[1]

    def step(self):
        """
        Update the point.
        """
        x_dot = -(self.mu * self.x) + (self.z * self.y)
        y_dot = -(self.mu * self.y) + self.x * (self.z - self.a)
        z_dot = 1 - (self.x * self.y)
        self.x += x_dot * self.dt
        self.y += y_dot * self.dt
        self.z += z_dot * self.dt


def get_attractors():
    return [Lorenz(), PanXuZhou(), Rikitake(), Rossler()]


class StrangeAttractor(EuroPiScript):
    def __init__(self):

        # Initialise and calculate ranges.
        # This will take around 30 seconds per unsaved attractor.
        self.attractors = get_attractors()
        self.init_estimates()

        # select a random attractor
        self.selected_attractor = choice(range(0, len(self.attractors)))
        self.a = self.attractors[self.selected_attractor]
        # Initialize variables
        self.checkpoint = 0
        # time before update
        self.period = 100
        # output range.
        self.range = MAX_OUTPUT
        # initial threshold for gates
        self.threshold = 20
        # freeze motion
        self.freeze = False
        # Display details
        self.show_detail = True

        # Triggered when button 1 is released
        # Short press: decrease range
        # Long press: change equation system
        @b1.handler_falling
        def b1Pressed():
            if ticks_diff(ticks_ms(), b1.last_pressed()) > 300:
                # long press This will result in a jump in parameters
                # as each attractor has its own x,y,z
                # coordinates. Possible improvement is to share or set
                # coordinates on change.
                self.selected_attractor = (self.selected_attractor + 1) % len(self.attractors)
                self.a = self.attractors[self.selected_attractor]
            else:
                # short press
                self.range -= 1
                if self.range < 1:
                    self.range = 1

        # Triggered when button 2 is released.
        # Short press: increase range
        # Long press: toggle display
        @b2.handler_falling
        def b2Pressed():

            if ticks_diff(ticks_ms(), b2.last_pressed()) > 300:
                # long press
                self.show_detail = not self.show_detail
            else:
                # short press
                self.range += 1
                if self.range > MAX_OUTPUT:
                    self.range = MAX_OUTPUT

        # Freeze is triggered when din goes HIGH.
        @din.handler
        def dinTrigger():
            # Pause
            self.freeze = True

        @din.handler_falling
        def dinTriggerEnd():
            # Start agin
            self.freeze = False

    def init_estimates(self):
        self.initialise_message()
        state = self.load_state_json()
        state_dirty = False
        for att in self.attractors:
            att_state = state.get(att.name)
            if att_state:
                att.set_range(
                    att_state.get("x_min"),
                    att_state.get("x_max"),
                    att_state.get("y_min"),
                    att_state.get("y_max"),
                    att_state.get("z_min"),
                    att_state.get("z_max"),
                )
            else:
                self.initialise_message(att.name)
                att.estimate_ranges()
                state[att.name] = {
                    "x_min": att.x_min,
                    "x_max": att.x_max,
                    "y_min": att.y_min,
                    "y_max": att.y_max,
                    "z_min": att.z_min,
                    "z_max": att.z_max,
                }
                state_dirty = True

        if state_dirty:
            self.save_state_json(state)

    def update_values(self):
        if not self.freeze:
            self.a.step()

    def update_speed(self):
        # Set speed based on the knob.
        # The range is piecewise linear from fully CCW to noon and noon to fully CW.
        # TODO: allow speed adjustment via CV.
        val = k1.read_position()
        low = 1000  # CCW
        mid = 100  # noon
        high = 10  # CW

        if val == 0:
            self.period = low
        elif val < 50:
            self.period = low - ((low - mid) * (val / 50))
        else:
            self.period = mid - ((mid - high) * (val - 50) / 50)

    def update_threshold(self):
        self.threshold = k2.read_position(steps=41)

    def update(self):
        # Change the values and output
        self.update_values()
        cv1.voltage((self.range * self.a.x_scaled()) / 100)
        cv2.voltage((self.range * self.a.y_scaled()) / 100)
        cv3.voltage((self.range * self.a.z_scaled()) / 100)
        # Calculate gates
        # gate 1 fires if x is divisible by 2 when considered an int
        self.gate4 = floor(self.a.x_scaled()) % 2 == 0
        # gates 2 and 3 look at the differences between the outputs.
        self.gate5 = (
            fabs(self.a.y_scaled() + self.a.z_scaled() - 2 * self.a.x_scaled()) > self.threshold
        )
        self.gate6 = (
            fabs(self.a.z_scaled() + self.a.x_scaled() - 2 * self.a.y_scaled()) > self.threshold
        )

        # Set gates
        cv4.value(self.gate4)
        cv5.value(self.gate5)
        cv6.value(self.gate6)

        self.checkpoint = ticks_ms()
        self.update_screen()

    def main(self):
        while True:
            self.update_speed()
            self.update_threshold()
            if ticks_diff(ticks_ms(), self.checkpoint) > self.period:
                self.update()

    def initialise_message(self, att_name=None):
        oled.fill(0)
        oled.text("Strange", 0, 0, 1)
        oled.text(f"Attractor v{VERSION}", 0, 8, 1)
        oled.text("Initialising...", 0, 16, 1)
        if att_name:
            oled.text(att_name, 10, 24, 1)
        oled.show()

    def update_screen(self):
        oled.fill(0)
        if self.show_detail:
            oled.text("1:" + str(int(self.a.x_scaled())), 0, 0, 1)
            oled.text("2:" + str(int(self.a.y_scaled())), 0, 8, 1)
            oled.text("3:" + str(int(self.a.z_scaled())), 0, 16, 1)
            oled.text("S:" + str(int(self.period)), 40, 0, 1)
            oled.text("T:" + str(int(self.threshold)), 40, 8, 1)
            oled.text("R:" + str(int(self.range)), 40, 16, 1)
        else:
            oled.text("1:", 0, 0, 1)
            oled.fill_rect(20, 0, int(0.75 * self.a.x_scaled()), 6, 1)
            oled.rect(20, 0, 75, 6, 1)
            oled.text("2:", 0, 8, 1)
            oled.fill_rect(20, 8, int(0.75 * self.a.y_scaled() / 2), 6, 1)
            oled.rect(20, 8, 75, 6, 1)
            oled.text("3:", 0, 16, 1)
            oled.fill_rect(20, 16, int(0.75 * self.a.z_scaled() / 2), 6, 1)
            oled.rect(20, 16, 75, 6, 1)

        if self.gate4:
            oled.text("4", 100, 0, 1)
        if self.gate5:
            oled.text("5", 100, 8, 1)
        if self.gate6:
            oled.text("6", 100, 16, 1)
        if self.freeze:
            oled.text("FREEZE", 0, 24, 1)
        oled.text(self.a.name, 55, 24, 1)

        oled.show()


if __name__ == "__main__":
    StrangeAttractor().main()