Spider Web

By the end of this lab you'll be able to:

• Draw radial spokes from the center using angles spaced 30° apart
• Connect the spokes with concentric polygonal rings using goto()
• Combine two loop types (radial and ring) to build a complete web

A realistic-looking spider web with 12 radial threads and 6 concentric rings — all drawn with goto() using polar coordinates converted to x, y.

Welcome to the Spider Web!

A spider web uses two geometric ideas: radial lines and concentric rings. This lab draws both using goto() and the math of circles! Let's code it together!

How It Works

Spokes: for each of 12 angles (0°, 30°, 60°, … 330°), draw a line from the center to radius 120. Rings: for each ring radius (20, 40, 60, 80, 100, 120), visit all 12 spoke intersection points and connect them.

Sample Code

import turtle
import math
monty = turtle.Turtle()
monty.speed(0)
monty.hideturtle()

n_spokes = 12
n_rings = 6
max_r = 120
angles = [i * 360 / n_spokes for i in range(n_spokes)]

monty.pencolor('gray')
monty.pensize(1)

for ang in angles:
    monty.penup()
    monty.goto(0, 0)
    monty.pendown()
    rad = math.radians(ang)
    monty.goto(max_r * math.cos(rad), max_r * math.sin(rad))

for ring in range(1, n_rings + 1):
    r = ring * max_r / n_rings
    monty.penup()
    rad0 = math.radians(angles[0])
    monty.goto(r * math.cos(rad0), r * math.sin(rad0))
    monty.pendown()
    for ang in angles[1:] + [angles[0]]:
        rad = math.radians(ang)
        monty.goto(r * math.cos(rad), r * math.sin(rad))

monty.penup()
monty.goto(0, 0)
monty.pendown()
monty.dot(10, 'black')

What Do You Think Will Happen?

We draw 12 spokes and 6 rings. How many polygon sides will each ring have? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

Each ring is a 12-sided polygon — one side per spoke. With 12 spokes equally spaced, each side spans 30°. Were you right?

How It Works

angles[1:] + [angles[0]] visits all 12 spokes then returns to the first — closing each ring polygon. r * math.cos(rad), r * math.sin(rad) converts polar (r, angle) to Cartesian (x, y).

Explanation Table

Line	What it does
angles = [i * 360 / n_spokes for i in range(n_spokes)]	12 equally spaced spoke angles
r = ring * max_r / n_rings	Ring radius increases evenly outward
angles[1:] + [angles[0]]	Visit all spokes, then close the ring
math.cos(rad), math.sin(rad)	Convert angle to x, y offset

Learning Check

Your Turn — Add More Spokes

Change n_spokes = 12 to n_spokes = 8. How many polygon sides will each ring have? Predict, then run it to check!

▶ Run ↻ Reset

8 spokes → 8-sided octagonal rings — each ring is now an octagon instead of a 12-sided polygon.

Experiments

1. Add a spider. After drawing, place a filled circle at (30, 30) using monty.dot(20, 'black'). You'll know it worked when a spider appears on the web.

2. Use concentric circles instead of polygons. Replace the ring-drawing code with monty.circle(r) at each ring radius. You'll know it worked when the rings look round.

3. Color the rings. Create a list of ring colors and use monty.pencolor(ring_colors[ring]). You'll know it worked when each ring is a different color.

4. Make the web asymmetric. Instead of equal spacing, use non-uniform angles. You'll know it worked when the web looks irregular like a real spider web.

Eight-Legged Geometry!

You drew a spider web using only polar coordinates and goto()! The combination of radial and ring structures appears everywhere in nature and engineering. Up next: Lightning Bolt — recursive jagged zigzag.