Working implementation of limacon rendering using turtle

limacons_working.py

from turtle import *
from math import pi,cos
color('blue', 'green')

#speedup
speed(0)
delay(0)
tracer(0,0)
penup()

def get_pos(i, t): # get position for each line draw step
    b = 1/30 * i
    a = 1 - (1/30 * i)
    r = b - a * cos(t*pi/180)
    r *= 200

    penup()
    left(t-90) # rotate 90 deg clockwise
    forward(r)
    pos_save = pos()
    home()
    
    return pos_save
    
for i in range(1,31): # 30 curves
    oldpos = get_pos(i,0)
    for t in range(91): # 90 steps per curve (t varies from 0 to 2pi)
        t*=4 # convert to 360deg
        newpos = get_pos(i,t)
        
        goto(oldpos)
        pendown()
        goto(newpos)
        penup()
        
        oldpos = newpos
        home()

hideturtle()
update() # draw all at once
done()