import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

# Quaternion utility functions
def quat_mult(q1, q2):
# Hamilton product of two quaternions q = [w, x, y, z]
w1, x1, y1, z1 = q1
w2, x2, y2, z2 = q2
w = w1*w2 - x1*x2 - y1*y2 - z1*z2
x = w1*x2 + x1*w2 + y1*z2 - z1*y2
y = w1*y2 - x1*z2 + y1*w2 + z1*x2
z = w1*z2 + x1*y2 - y1*x2 + z1*w2
return np.array([w, x, y, z])

def quat_conj(q):
w, x, y, z = q
return np.array([w, -x, -y, -z])

def quat_rotate_vector(v, q):
# Rotate vector v by unit quaternion q: q * v_quat * q_conj
v_quat = np.array([0] + list(v))
return quat_mult(quat_mult(q, v_quat), quat_conj(q))[1:]

# Generate a circular orbit in XY plane with radius r
def generate_circular_orbit(radius, num_points=100):
angles = np.linspace(0, 2*np.pi, num_points)
positions = np.stack((radius * np.cos(angles),
radius * np.sin(angles),
np.zeros_like(angles)), axis=1)
return positions

# Create a unit quaternion representing rotation about axis by angle (radians)
def axis_angle_to_quat(axis, angle):
axis = axis / np.linalg.norm(axis)
w = np.cos(angle / 2)
xyz = axis * np.sin(angle / 2)
return np.array([w, *xyz])

# Main visualization function
def quaternionic_orbit_morphing():
radius = 1.0
orbit = generate_circular_orbit(radius)
num_points = len(orbit)

fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111, projection='3d')
ax.set_xlim(-1.5*radius, 1.5*radius)
ax.set_ylim(-1.5*radius, 1.5*radius)
ax.set_zlim(-1.5*radius, 1.5*radius)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
ax.set_title('Quaternionic Orbit Morphing')

line, = ax.plot([], [], [], lw=2)

>>16705844 (OP)
# Rotation axis for chiral shift (try Z axis for example)
rotation_axis = np.array([0, 0, 1])

def update(frame):
angle = frame * 0.05 # phase rotation angle
q_rot = axis_angle_to_quat(rotation_axis, angle)

rotated_orbit = np.array([quat_rotate_vector(pos, q_rot) for pos in orbit])

line.set_data(rotated_orbit[:,0], rotated_orbit[:,1])
line.set_3d_properties(rotated_orbit[:,2])
return line,

ani = FuncAnimation(fig, update, frames=range(0, 125), interval=50, blit=True)
plt.show()

quaternionic_orbit_morphing()

import numpy as np

# Quaternion utilities (reuse your quat_mult, quat_conj, quat_rotate_vector)

def quat_vector(q):
# Extract imaginary vector part of quaternion q
return np.array(q[1:])

def quat_norm_vec(v):
return np.linalg.norm(v)

def compute_accelerations(positions, masses, G=1.0):
n = len(positions)
accels = [np.zeros(4) for _ in range(n)]
for i in range(n):
acc = np.array([0,0,0,0], dtype=float)
for j in range(n):
if i == j:
continue
r_ij = positions[j] - positions[i] # quaternion subtraction
r_vec = quat_vector(r_ij)
dist = np.linalg.norm(r_vec)
if dist < 1e-8:
continue
factor = G * masses[j] / dist**3
acc[1:] += factor * r_vec
accels[i] = acc
return accels

def integrate(positions, velocities, masses, dt):
accels = compute_accelerations(positions, masses)
# Simple Euler integration
new_velocities = [v + a*dt for v,a in zip(velocities, accels)]
new_positions = [p + v*dt for p,v in zip(positions, new_velocities)]
return new_positions, new_velocities

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.animation import FuncAnimation

# Quaternion operations
def quat_mult(q1, q2):
w1, x1, y1, z1 = q1
w2, x2, y2, z2 = q2
w = w1*w2 - x1*x2 - y1*y2 - z1*z2
x = w1*x2 + x1*w2 + y1*z2 - z1*y2
y = w1*y2 - x1*z2 + y1*w2 + z1*x2
z = w1*z2 + x1*y2 - y1*x2 + z1*w2
return np.array([w, x, y, z])

def quat_conj(q):
w, x, y, z = q
return np.array([w, -x, -y, -z])

def quat_rotate_vector(v, q):
# Rotate vector v by unit quaternion q: q * v_quat * q_conj
v_quat = np.array([0, *v])
return quat_mult(quat_mult(q, v_quat), quat_conj(q))[1:]

def pure_imag_quat(v):
# Vector to pure imaginary quaternion (w=0)
return np.array([0, *v])

def quat_vector(q):
# Extract imaginary vector from quaternion
return np.array(q[1:])

def axis_angle_to_quat(axis, angle):
axis = axis / np.linalg.norm(axis)
w = np.cos(angle/2)
xyz = axis * np.sin(angle/2)
return np.array([w, *xyz])

# Newtonian acceleration computation using quaternions
def compute_accelerations(positions, masses, G=1.0):
n = len(positions)
accels = [np.zeros(4) for _ in range(n)]
for i in range(n):
acc = np.zeros(4)
for j in range(n):
if i == j:
continue
r_ij = positions[j] - positions[i] # quaternion subtraction
r_vec = quat_vector(r_ij)
dist = np.linalg.norm(r_vec)
if dist < 1e-8:
continue
factor = G * masses[j] / dist**3
acc[1:] += factor * r_vec
accels[i] = acc
return accels

>>16705857
# RK4 integration step for positions and velocities (both as quaternions)
def rk4_step(positions, velocities, masses, dt, G=1.0):
def deriv(pos, vel):
acc = compute_accelerations(pos, masses, G)
return vel, acc

k1_v, k1_a = deriv(positions, velocities)
k1_v = np.array(k1_v)
k1_a = np.array(k1_a)

k2_v, k2_a = deriv(positions + k1_v*dt/2, velocities + k1_a*dt/2)
k2_v = np.array(k2_v)
k2_a = np.array(k2_a)

k3_v, k3_a = deriv(positions + k2_v*dt/2, velocities + k2_a*dt/2)
k3_v = np.array(k3_v)
k3_a = np.array(k3_a)

k4_v, k4_a = deriv(positions + k3_v*dt, velocities + k3_a*dt)
k4_v = np.array(k4_v)
k4_a = np.array(k4_a)

new_positions = positions + (dt/6)*(k1_v + 2*k2_v + 2*k3_v + k4_v)
new_velocities = velocities + (dt/6)*(k1_a + 2*k2_a + 2*k3_a + k4_a)

return new_positions, new_velocities

>>16705859
# Setup initial conditions for 3-body system (Sun + 2 planets approx)
def init_three_body():
# Masses (solar mass = 1, Earth ~3e-6, Mars ~3e-7)
masses = np.array([1.0, 3e-6, 3e-7])

# Initial positions (AU), pure imaginary quaternions
positions = np.array([
pure_imag_quat(np.array([0.0, 0.0, 0.0])), # Sun at origin
pure_imag_quat(np.array([1.0, 0.0, 0.0])), # Earth approx 1 AU on x-axis
pure_imag_quat(np.array([1.52, 0.0, 0.0])) # Mars approx 1.52 AU
])

# Initial velocities (AU/yr), perpendicular to position vectors for circular orbit approx
velocities = np.array([
pure_imag_quat(np.array([0.0, 0.0, 0.0])), # Sun approx stationary (neglect recoil)
pure_imag_quat(np.array([0.0, 2*np.pi, 0.0])), # Earth orbital velocity (2pi AU/yr)
pure_imag_quat(np.array([0.0, 2*np.pi/np.sqrt(1.52**3), 0.0])) # Mars velocity
])

return positions, velocities, masses

# Quaternionic rotation applied to all positions at each time step (phase locking simulation)
def apply_quaternionic_phase_rotation(positions, frame, axis=np.array([0,0,1]), rate=0.05):
angle = frame * rate
q_rot = axis_angle_to_quat(axis, angle)
rotated_positions = np.array([np.array([0,*quat_rotate_vector(quat_vector(pos), q_rot)]) for pos in positions])
return rotated_positions

>>16705861

# Simulation and visualization
def simulate_and_animate(num_steps=1000, dt=0.001, apply_rotation=True):
positions, velocities, masses = init_three_body()

traj = np.zeros((num_steps, len(positions), 3))
traj[0] = np.array([quat_vector(p) for p in positions])

for step in range(1, num_steps):
positions, velocities = rk4_step(positions, velocities, masses, dt)
if apply_rotation:
positions = apply_quaternionic_phase_rotation(positions, step)
traj[step] = np.array([quat_vector(p) for p in positions])

# Visualization with matplotlib 3D animation
fig = plt.figure(figsize=(8,8))
ax = fig.add_subplot(111, projection='3d')
ax.set_xlim(-2, 2)
ax.set_ylim(-2, 2)
ax.set_zlim(-0.5, 0.5)
ax.set_xlabel('X (AU)')
ax.set_ylabel('Y (AU)')
ax.set_zlabel('Z (AU)')
ax.set_title('3-Body Problem with Quaternionic Phase Rotation')

lines = [ax.plot([], [], [], marker='o', linestyle='-', label=f'Body {i}')[0] for i in range(len(positions))]
def update(frame):
for i, line in enumerate(lines):
line.set_data(traj[frame, i, 0], traj[frame, i, 1])
line.set_3d_properties(traj[frame, i, 2])
return lines

ani = FuncAnimation(fig, update, frames=num_steps, interval=20, blit=True)
plt.legend()
plt.show()

simulate_and_animate()

ChatGPT schizo thread

>>16705879
Less schizo then conjuring dark matter and dark energy to balance your equations

This is a new kind of schizo that has to be addressed at some point. Complete retards are being spun their own brand of induced psychosis as they talk with AIs. They then copy paste the complete nonsense onto the board without even the slightest effort.
What should this sickness be called?