Drawing a Birthday Cake with Python Turtle Graphics

The author was inspired by a hand‑drawn cake seen on Bilibili and decided to recreate it programmatically using Python's turtle graphics library.

The script imports turtle , math , and random , defines helper functions drawX and drawY to compute parametric coordinates, configures the drawing canvas, and then draws a series of layered shapes with various fill colors to form a stylized cake, adds random decorative dots, and writes a "Happy Birthday" message.

<code>import turtle as t
import math as m
import random as r

def drawX(a, i):
    angle = m.radians(i)
    return a * m.cos(angle)

def drawY(b, i):
    angle = m.radians(i)
    return b * m.sin(angle)
# 设置背景颜色，窗口位置以及大小
t.bgcolor("#d3dae8")
t.setup(1000, 800)
t.penup()
t.goto(150, 0)
t.pendown()
# 1
t.pencolor("white")
t.begin_fill()
for i in range(360):
    x = drawX(150, i)
    y = drawY(60, i)
    t.goto(x, y)
    t.fillcolor("#fef5f7")
    t.end_fill()
# 2
t.begin_fill()
for i in range(180):
    x = drawX(150, -i)
    y = drawY(70, -i)
    t.goto(x, y)
for i in range(180, 360):
    x = drawX(150, i)
    y = drawY(60, i)
    t.goto(x, y)
    t.fillcolor("#f2d7dd")
    t.end_fill()
# 3
t.pu()
 t.goto(120, 0)
 t.pd()
 t.begin_fill()
for i in range(360):
    x = drawX(120, i)
    y = drawY(48, i)
    t.goto(x, y)
    t.fillcolor("#cbd9f9")
    t.end_fill()
# 4
t.begin_fill()
 t.pencolor("#fee48c")
 for i in range(540):
    x = drawX(120, i)
    y = drawY(48, i) + 70
    t.goto(x, y)
 t.goto(-120, 0)
 t.fillcolor("#cbd9f9")
 t.end_fill()
# 5
t.pu()
 t.goto(120, 70)
 t.pd()
 t.pencolor("#fff0f3")
 t.begin_fill()
 for i in range(360):
    x = drawX(120, i)
    y = drawY(48, i) + 70
    t.goto(x, y)
    t.fillcolor("#fff0f3")
    t.end_fill()
# 6
t.pu()
 t.goto(110, 70)
 t.pd()
 t.pencolor("#fff9fb")
 t.begin_fill()
 for i in range(360):
    x = drawX(110, i)
    y = drawY(44, i) + 70
    t.goto(x, y)
    t.fillcolor("#fff9fb")
    t.end_fill()
# 7
t.pu()
 t.goto(120, 0)
 t.pd()
 t.begin_fill()
 t.pencolor("#ffa79d")
 for i in range(180):
    x = drawX(120, -i)
    y = drawY(48, -i) + 10
    t.goto(x, y)
 t.goto(-120, 0)
 for i in range(180, 360):
    x = drawX(120, i)
    y = drawY(48, i)
    t.goto(x, y)
    t.fillcolor("#ffa79d")
    t.end_fill()
# 8
t.pu()
 t.goto(120, 70)
 t.pd()
 t.begin_fill()
 t.pensize(4)
 t.pencolor("#fff0f3")
 for i in range(1800):
    x = drawX(120, 0.1 * i)
    y = drawY(-18, i) + 10
    t.goto(x, y)
 t.goto(-120, 70)
 t.pensize(1)
 for i in range(180, 360):
    x = drawX(120, i)
    y = drawY(48, i) + 70
    t.goto(x, y)
    t.fillcolor("#fff0f3")
    t.end_fill()
# 9
t.pu()
 t.goto(80, 70)
 t.pd()
 t.begin_fill()
 t.pencolor("#6f3732")
 t.goto(80, 120)
 for i in range(180):
    x = drawX(80, i)
    y = drawY(32, i) + 120
    t.goto(x, y)
 t.goto(-80, 70)
 for i in range(180, 360):
    x = drawX(80, i)
    y = drawY(32, i) + 70
    t.goto(x, y)
    t.fillcolor("#6f3732")
    t.end_fill()
# 10
t.pu()
 t.goto(80, 120)
 t.pd()
 t.pencolor("#ffaaa0")
 t.begin_fill()
 for i in range(360):
    x = drawX(80, i)
    y = drawY(32, i) + 120
    t.goto(x, y)
    t.fillcolor("#ffaaa0")
    t.end_fill()
# 11
t.pu()
 t.goto(70, 120)
 t.pd()
 t.pencolor("#ffc3be")
 t.begin_fill()
 for i in range(360):
    x = drawX(70, i)
    y = drawY(28, i) + 120
    t.goto(x, y)
    t.fillcolor("#ffc3be")
    t.end_fill()
# 12
t.pu()
 t.goto(80, 120)
 t.pd()
 t.begin_fill()
 t.pensize(3)
 t.pencolor("#ffaaa0")
 for i in range(1800):
    x = drawX(80, 0.1 * i)
    y = drawY(-12, i) + 80
    t.goto(x, y)
 t.goto(-80, 120)
 t.pensize(1)
 for i in range(180, 360):
    x = drawX(80, i)
    y = drawY(32, i) + 120
    t.goto(x, y)
    t.fillcolor("#ffaaa0")
    t.end_fill()
# 13
t.pu()
 t.goto(64, 120)
 t.pd()
 t.pencolor("#b1c9e9")
 t.begin_fill()
 for i in range(360):
    x = drawX(4, i) + 60
    y = drawY(1, i) + 120
    t.goto(x, y)
 t.goto(64, 170)
 for i in range(540):
    x = drawX(4, i) + 60
    y = drawY(1, i) + 170
    t.goto(x, y)
    t.goto(56, 120)
    t.fillcolor("#b1c9e9")
    t.end_fill()
 t.pencolor("white")
 t.pensize(2)
 for i in range(1, 6):
    t.goto(64, 120 + 10 * i)
    t.pu()
    t.goto(56, 120 + 10 * i)
    t.pd()
# 14
color = ["#e28cb9", "#805a8c", "#eaa989", "#6e90b7", "#b8b68f", "#e174b5", "#cf737c", "#7c8782"]
for i in range(80):
    t.pu()
    x = r.randint(-120, 120)
    y = r.randint(-25, 30)
    t.goto(x, y)
    t.pd()
    t.dot(r.randint(2, 5), color[r.randint(0, 7)])
for i in range(40):
    t.pu()
    x = r.randint(-90, 90)
    y = r.randint(-35, 10)
    t.goto(x, y)
    t.pd()
    t.dot(r.randint(2, 5), color[r.randint(0, 7)])
for i in range(40):
    t.pu()
    x = r.randint(-80, 80)
    y = r.randint(60, 90)
    t.goto(x, y)
    t.pd()
    t.dot(r.randint(2, 5), color[r.randint(0, 7)])
for i in range(30):
    t.pu()
    x = r.randint(-50, 50)
    y = r.randint(45, 70)
    t.goto(x, y)
    t.pd()
    t.dot(r.randint(2, 5), color[r.randint(0, 7)])
# Random dots
for i in range(50):
    t.pu()
    x = r.randint(-500, 500)
    y = r.randint(120, 300)
    t.goto(x, y)
    t.pd()
    t.dot(r.randint(3, 5), color[r.randint(0, 7)])
 t.seth(90)
 t.pu()
 t.goto(0, 0)
 t.fd(210)
 t.left(90)
 t.fd(170)
 t.pd()
 t.write("Happy Birthday", font=("Curlz MT", 50))
 t.done()</code>

The resulting image (shown in the attached screenshot) demonstrates the cake drawing, and the author reflects that the code is repetitive and could be refactored, encouraging readers to apply parametric equations and improve coding practices.