Equation of Logarithmic Spiral That Goes Through Given Points

Question

Suppose I generate the following list of points:

0 (5.00000, 15.00000)
1 (5.00000, -1.66667)
2 (-0.55556, -1.66667)
3 (-0.55556, 0.18519)
4 (0.06173, 0.18519)
5 (0.06173, -0.02058)
6 (-0.00686, -0.02058)
7 (-0.00686, 0.00229)
8 (0.00076, 0.00229)
9 (0.00076, -0.00025)
10 (-0.00008, -0.00025)
11 (-0.00008, 0.00003)
12 (0.00001, 0.00003)
13 (0.00001, -0.00000)
14 (-0.00000, -0.00000)

Which looks like this:

What is the equation of the continuous logarithmic spiral that goes through all of those points? Either parametric or polar is fine.

For reference, this is the Python code I used to generate those points:

import math
start_x = -45 
start_y = 15
points = [(start_x,start_y)]
for ii in range(20):
  
  if ii%4 == 0:
    start_x += 50*math.exp(-ii*math.log(3))
  elif ii%4 == 1:
    start_y -= 50*math.exp(-ii*math.log(3))
  elif ii%4 == 2:
    start_x -= 50*math.exp(-ii*math.log(3))
  else:
    start_y += 50*math.exp(-ii*math.log(3))
  print(ii, f'({start_x:.5f}, {start_y:.5f})')
  points.append((start_x,start_y))