# Each dynamical system can be a child of this parent class
class DynamicalSystem:
def __init__(self, initial_conditions):
self.state = initial_conditions

def update(self, external_influence):
# Update state based on system's dynamics and external influences
raise NotImplementedError

def output_state(self):
return self.state

class LorenzSystem(DynamicalSystem):
def __init__(self, initial_conditions, t, sigma=10, rho=28, beta=8/3):
super().__init__(initial_conditions)
self.t = t
self.sigma = sigma
self.rho = rho
self.beta = beta

def lorenz(self, X, t):
x, y, z = X
dx_dt = self.sigma * (y - x)
dy_dt = x * (self.rho - z) - y
dz_dt = x * y - self.beta * z
return dx_dt, dy_dt, dz_dt

def update(self, external_influence):
# Update state based on Lorenz dynamics and external influences
self.state = odeint(self.lorenz, self.state + external_influence, self.t)

def visualize(self):
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(self.state[:, 0], self.state[:, 1], self.state[:, 2])
plt.show()

# The controller class handles creating, updating, and destroying systems
class SystemController:
def __init__(self):
self.systems = []

def add_system(self, system):
self.systems.append(system)

def remove_system(self, system):
self.systems.remove(system)

def update_all(self, influences):
for system, influence in zip(self.systems, influences):
system.update(influence)

from abc import ABC, abstractmethod
from scipy.integrate import odeint
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

# Abstract Base class for dynamical systems
class DynamicalSystem(ABC):
def __init__(self, initial_conditions):
self.state = initial_conditions

@abstractmethod
def update(self, external_influence):
pass

def output_state(self):
return self.state

class LorenzSystem(DynamicalSystem):
def __init__(self, initial_conditions, t, sigma=10, rho=28, beta=8/3):
super().__init__(initial_conditions)
self.t = t
self.sigma = sigma
self.rho = rho
self.beta = beta

def lorenz(self, X, t):
x, y, z = X
dx_dt = self.sigma * (y - x)
dy_dt = x * (self.rho - z) - y
dz_dt = x * y - self.beta * z
return dx_dt, dy_dt, dz_dt

def update(self, external_influence):
self.state = odeint(self.lorenz, self.state + external_influence, self.t)

class SystemController:
def __init__(self):
self.systems = []

def add_system(self, system: DynamicalSystem):
self.systems.append(system)

def remove_system(self, system: DynamicalSystem):
self.systems.remove(system)

def update_all(self, influences):
self.systems = [system.update(influence) for system, influence in zip(self.systems, influences)]

def apply_interactions(self, interaction_matrix):
influences = [sum(interaction * other.output_state() for interaction, other in zip(row, self.systems)) for row in interaction_matrix]
self.update_all(influences)

class SystemVisualizer:
@staticmethod
def visualize(system: LorenzSystem):
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(system.state[:, 0], system.state[:, 1], system.state[:, 2])
plt.show()


class DataMorphogeneticOrganism:
def __init__(self, df, initial_conditions, t):
self.data_handler = DataAndDiffHandler(df)
self.system_controller = SystemController()
self.initial_conditions = initial_conditions
self.t = t

def preprocess_data(self):
self.data_handler.preprocess()

def add_system(self, sigma=10, rho=28, beta=8/3):
system = LorenzSystem(self.initial_conditions, self.t, sigma, rho, beta)
self.system_controller.add_system(system)

def remove_system(self, system: LorenzSystem):
self.system_controller.remove_system(system)

def update_systems(self, influences):
self.system_controller.update_all(influences)

def apply_interactions(self, interaction_matrix):
self.system_controller.apply_interactions(interaction_matrix)

def visualize_system(self, system: LorenzSystem):
SystemVisualizer.visualize(system)
DataMorphogeneticOrganism Documentation
Overview
The DataMorphogeneticOrganism is a bio-inspired computational system aimed at simulating dynamical systems and enabling their interaction, adaptation, and evolution over time. This versatile system integrates capabilities for data preprocessing, dynamical system simulation, and interaction of multiple systems.

Components
1. DataAndDiffHandler
Methods:
__init__(self, df=None): Constructor for the DataAndDiffHandler. Takes an optional df argument representing a pandas DataFrame.

preprocess(self): Handles missing data, removes duplicates, and normalizes the DataFrame. Returns the preprocessed DataFrame.

differential(self, func, var, order): Computes the differential of the given function func with respect to variable var of order order.

create_tensor(self, diff1, diff2): Converts the given differentials diff1 and diff2 into a tensor.

2. DynamicalSystem
Methods:
__init__(self, initial_conditions): Constructor for the DynamicalSystem class. Takes initial conditions for the dynamical system.

update(self, external_influence): Abstract method to be overridden in subclasses. Updates the state of the system based on external influences.

output_state(self): Returns the current state of the dynamical system.

3. LorenzSystem
A subclass of DynamicalSystem that simulates the Lorenz system.

Methods:
__init__(self, initial_conditions, t, sigma=10, rho=28, beta=8/3): Constructor for the LorenzSystem. Takes initial conditions, time points t, and optional parameters sigma, rho, beta.

lorenz(self, X, t): Implements the Lorenz equations.

update(self, external_influence): Updates the state of the Lorenz system with respect to external influences.

4. SystemController
Methods:
__init__(self): Constructor for the SystemController class.

add_system(self, system): Adds a DynamicalSystem to the system controller.

remove_system(self, system): Removes a DynamicalSystem from the system controller.

update_all(self, influences): Updates all systems within the system controller based on their respective influences.

apply_interactions(self, interaction_matrix): Applies interactions between different systems using the given interaction matrix.

5. SystemVisualizer
Methods:
visualize(system): Visualizes the state of a LorenzSystem in 3D space.
Use Cases
The DataMorphogeneticOrganism is versatile and can be employed in a variety of contexts. Some key use cases include:

Data Cleaning and Normalization
Simulating and Visualizing Dynamical Systems
Interacting Different Dynamical Systems
Performing Differential Analysis
Creating Tensors from Differentials
Responding to External Influences
Decoupling Systems
Implementing Bio-Inspired Computing Paradigms