EC is a spiral curve like spring

try this 3d graph generator:



import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import numpy as np

# parameters
p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
a = 0
b = 7
Gx = 55066263022277343669578718895168534326250603453777594175500187360389116729240
Gy = 32670510020758816978083085130507043184471273380659243275938904335757337482424

# start + end decimal key
start = int(input("input start key: "))
end = int(input("input end key: "))

# generation
x = []
y = []
z = []
for i in range(start, end + 1):
    # point calculation index i
    Px = i * Gx
    Py = i * Gy
    x.append(Px % p)
    y.append(Py % p)
    z.append(i)

# 3D chart
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.plot(x, y, z, c='r', linewidth=2)

# add points on chart
for i, (xi, yi, zi) in enumerate(zip(x, y, z)):
    ax.text(xi, yi, zi, str(i), color='blue')

ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Index')
ax.set_title('point on elliptic curve secp256k1 (3D graph)')

plt.show()