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a0589da | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | import decimal
from decimal import Decimal, getcontext
# Set the precision
getcontext().prec = 110
# Constants
c = 299792458 # Speed of light in m/s
h = Decimal('6.62607015e-34') # Planck constant in J*s
k_B = Decimal('1.38e-23') # Boltzmann constant in J/K
TSR = Decimal(c**2) / k_B # Temperature to Speed Ratio in K*m/s
Q = Decimal('2') ** (Decimal('1') / Decimal('12')) # Fractal structure parameter
def chudnovsky_pi(n_terms):
C = Decimal(426880) * Decimal(10005).sqrt()
K = Decimal(6)
M = Decimal(1)
X = Decimal(1)
L = Decimal(13591409)
S = Decimal(0) # Initialize S to 0
for i in range(1, n_terms + 1): # Change to n_terms + 1 to avoid i = 0
if i == 1: # Handle the first iteration separately
M = Decimal(1) # Set M to 1 for the first iteration
else:
divisor = Decimal((i-1)**3)
if divisor == Decimal(0): # Check for zero divisor
divisor = Decimal(1) # Set divisor to 1 to avoid division by zero
M = (K**3 - Decimal(16)*K) * M // divisor
L += Decimal(545140134)
X *= Decimal(-262537412640768000)
term = Decimal(M * L) / X
# Apply fractal Q to the term
term *= Q ** (Decimal(i) / Decimal(n_terms))
# Apply TSR and quantum fluctuations conservatively
if term < Decimal('1e-15'):
TSR_rel = TSR
ΔTSR_q = Decimal('0')
else:
TSR_rel = TSR / Decimal((1 - (term**2 / Decimal(c**2))).sqrt())
ΔTSR_q = h * term
S += term * TSR_rel + ΔTSR_q
K += Decimal(12)
pi = C / S
return +pi
# Example usage
pi = chudnovsky_pi(100)
print(f"π ≈ {pi}")
# Save results to a JSON file
import json
with open('pi_simulation_results.json', 'w') as f:
json.dump({"pi_approx": str(pi)}, f)
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