Here is what the following code snippet draws; it is not an absolutely perfect reproduction of the gif you posted (some tweaks for the size progression for 3, 4, and 5-gons must be done to avoid the smaller neighbors to touch at some points – i/e the gif maker somewhat cheated!), but it follows mathematical symmetry and perfection.

The following code has some magic numbers; I may come back to it later, but not at this time. The resources I used to calculate a regular polygon can be found here, and there.

```
import turtle
import math
def reg_polygon(start_pos, number_of_angles, side):
interior_angle = (180 * (number_of_angles - 2)) / number_of_angles
turtle.setheading(180 - interior_angle//2)
for i in range(number_of_angles):
turtle.forward(side)
turtle.left(180 - interior_angle)
def reset_start_point():
global start_pos, startx, starty, initial_size, number_of_angles, side
startx += 8
starty -= 0
initial_size += 8
number_of_angles += 1
side = 2 * initial_size * math.sin(math.radians(180/number_of_angles))
start_pos = startx, starty
turtle.penup()
turtle.goto((startx, starty))
turtle.pendown()
start_pos = startx, starty = 0, 0
number_of_angles = 2
initial_size = 15 # radius
side = 0
while number_of_angles < 21:
reset_start_point()
reg_polygon(start_pos, number_of_angles, side)
turtle.done()
```

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