Drawing a Birthday Cake with Python Turtle Graphics

Introduction: The author was inspired by a hand‑drawn cake on Bilibili and decided to recreate it using Python after learning the turtle module.

Code implementation: The full turtle script is provided, showing imports, helper functions drawX and drawY , background setup, and a series of drawing steps (1‑17) that create the cake layers, decorations, and a “Happy Birthday” text. The code is presented unchanged within tags.</p><pre><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() Visual result: An image of the rendered cake is included, and a brief note mentions a video demonstration (not uploaded). Summary points: The current code contains many repetitions and could be refactored for elegance. Drawing arbitrary curves required understanding of parametric equations; the author considered Fourier transforms but used simple parametric functions instead. The turtle goto function uses a Cartesian coordinate system, enabling the use of high‑school level parametric equations for custom shapes. Conclusion: The example highlights the importance of mathematics in programming graphics.