Make Gas Function Smoother

[adamkrellenstein]

import matplotlib.pyplot as plt
import numpy as np
import math

k = .2 # Sigmoid Steepness
m = 1.5 # Exponent
n = 100 # Exponential Scaling Factor


def calculate_fee(x, a, b, base_fee):

    def sigmoid(t):
        midpoint = (b - a) / 2 + a
        return base_fee / (1 + math.exp(-k * (t - midpoint)))

    if x <= a:
        return 0
    elif x <= b:
        return sigmoid(x)
    else:
        return base_fee + ((x-b)**(m))/n

# Parameters
a = 3
b = 15
base_fee = 1
k = 1

# Generate values for x
x_values = np.linspace(0, 40, num=5000)
y_values = [calculate_fee(x, a, b, base_fee) for x in x_values]

# Plot the function
plt.plot(x_values, y_values, label='Fee Curve')
plt.axvline(x=a, color='r', linestyle='--', label='Lower Threshold (a)')
plt.axvline(x=b, color='g', linestyle='--', label='Upper Threshold (b)')
plt.xlabel('Number of Transactions per Period (x)')
plt.ylabel('Calculated Fee')
plt.title('Fee Curve for a = 3, b = 15, base_fee = 1, k = 10')
plt.legend()
plt.grid(True)
plt.show()

We should also add some rounding, I think.