chaos machine Algorithm
The Chaos Machine Algorithm is a computational paradigm that utilizes the principles of chaos theory and non-linear dynamics to model complex systems, solve optimization problems, and aid in decision-making processes. This algorithm is inspired by the natural phenomena of chaotic systems, such as weather patterns, turbulent fluid flows, and population dynamics, which are characterized by their sensitivity to initial conditions, unpredictability, and the presence of a wide range of scales. By harnessing the inherent properties of chaos, this algorithm is capable of exploring large and high-dimensional search spaces effectively, escaping local optima, and converging towards global optima in an efficient manner.
In the Chaos Machine Algorithm, the search process is guided by chaotic maps or chaotic sequences that are generated using mathematical functions exhibiting chaotic behavior, such as the logistic map, sine map, or tent map. These chaotic sequences provide a rich source of diversity and randomness, which enables the algorithm to explore the solution space thoroughly and adaptively. Moreover, the algorithm employs the concept of ergodicity, which ensures that the chaotic sequences visit all regions of the search space with equal probability, thus enhancing the overall effectiveness of the search process. The Chaos Machine Algorithm has been successfully applied to various domains, including optimization, machine learning, image processing, and control systems, demonstrating its versatility and potential in addressing complex real-world problems.
"""example of simple chaos machine"""
# Chaos Machine (K, t, m)
K = [0.33, 0.44, 0.55, 0.44, 0.33]
t = 3
m = 5
# Buffer Space (with Parameters Space)
buffer_space, params_space = [], []
# Machine Time
machine_time = 0
def push(seed):
global buffer_space, params_space, machine_time, K, m, t
# Choosing Dynamical Systems (All)
for key, value in enumerate(buffer_space):
# Evolution Parameter
e = float(seed / value)
# Control Theory: Orbit Change
value = (buffer_space[(key + 1) % m] + e) % 1
# Control Theory: Trajectory Change
r = (params_space[key] + e) % 1 + 3
# Modification (Transition Function) - Jumps
buffer_space[key] = round(float(r * value * (1 - value)), 10)
params_space[key] = r # Saving to Parameters Space
# Logistic Map
assert max(buffer_space) < 1
assert max(params_space) < 4
# Machine Time
machine_time += 1
def pull():
global buffer_space, params_space, machine_time, K, m, t
# PRNG (Xorshift by George Marsaglia)
def xorshift(X, Y):
X ^= Y >> 13
Y ^= X << 17
X ^= Y >> 5
return X
# Choosing Dynamical Systems (Increment)
key = machine_time % m
# Evolution (Time Length)
for i in range(0, t):
# Variables (Position + Parameters)
r = params_space[key]
value = buffer_space[key]
# Modification (Transition Function) - Flow
buffer_space[key] = round(float(r * value * (1 - value)), 10)
params_space[key] = (machine_time * 0.01 + r * 1.01) % 1 + 3
# Choosing Chaotic Data
X = int(buffer_space[(key + 2) % m] * (10 ** 10))
Y = int(buffer_space[(key - 2) % m] * (10 ** 10))
# Machine Time
machine_time += 1
return xorshift(X, Y) % 0xFFFFFFFF
def reset():
global buffer_space, params_space, machine_time, K, m, t
buffer_space = K
params_space = [0] * m
machine_time = 0
if __name__ == "__main__":
# Initialization
reset()
# Pushing Data (Input)
import random
message = random.sample(range(0xFFFFFFFF), 100)
for chunk in message:
push(chunk)
# for controlling
inp = ""
# Pulling Data (Output)
while inp in ("e", "E"):
print("%s" % format(pull(), "#04x"))
print(buffer_space)
print(params_space)
inp = input("(e)exit? ").strip()