Lightning Bolt

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

• Use recursion to split a straight line into a jagged zigzag
• Understand how branching recursion creates natural-looking electricity shapes
• Control depth and displacement to vary the jaggedness of the bolt

A simulated lightning bolt drawn by recursively replacing each straight segment with a bent, zigzagged version. The result is an irregular, branching shape that closely mimics real lightning.

Welcome to the Lightning Bolt!

Real lightning follows the path of least electrical resistance. The result looks random — but it has a recursive pattern we can code! Let's code it together!

How It Works

lightning(x1, y1, x2, y2, depth) splits the segment into two halves with the midpoint displaced sideways by a random amount. At depth 0, just draw the segment. At each depth, the displacement shrinks, creating self-similar jaggedness.

Sample Code

import turtle
import math
import random
monty = turtle.Turtle()
monty.speed(0)
monty.hideturtle()
turtle.bgcolor('black')
random.seed(7)

def lightning(x1, y1, x2, y2, depth):
    if depth == 0:
        monty.penup()
        monty.goto(x1, y1)
        monty.pendown()
        monty.goto(x2, y2)
        return
    mx = (x1 + x2) / 2
    my = (y1 + y2) / 2
    dx = x2 - x1
    dy = y2 - y1
    perp_x = -dy * 0.3
    perp_y = dx * 0.3
    offset = random.uniform(-1, 1)
    mx += perp_x * offset
    my += perp_y * offset
    monty.pencolor('yellow')
    monty.pensize(max(1, depth))
    lightning(x1, y1, mx, my, depth - 1)
    lightning(mx, my, x2, y2, depth - 1)

lightning(-50, 150, 50, -150, 5)

What Do You Think Will Happen?

We start with a vertical line and split it 5 levels deep. Will the result look like a straight line, a zigzag, or real lightning? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

A jagged lightning bolt — the recursive displacement creates the irregular, branching shape. Were you right?

How It Works

The perpendicular vector (-dy, dx) is perpendicular to (dx, dy) — rotating 90°. Multiplying by 0.3 limits displacement to 30% of the segment length. random.uniform(-1, 1) picks a random side. The recursion makes each sub-segment equally jagged.

Explanation Table

Line	What it does
if depth == 0	Base case: draw the segment
mx, my = midpoint	Find the midpoint to displace
perp_x = -dy * 0.3	Perpendicular displacement direction
random.uniform(-1, 1)	Random side and amount
pensize(max(1, depth))	Thicker lines at lower depth (main bolt)

Learning Check

Your Turn — Change the Depth

Change depth=5 to depth=3. The bolt will have fewer bends. Then try depth=7. Predict what changes at each depth!

▶ Run ↻ Reset

Depth 7 produces a much more detailed, realistic bolt with tiny jags everywhere.

Experiments

1. Remove the seed. Delete random.seed(7). Every run produces a different bolt. You'll know it worked when the bolt changes each time.

2. Draw multiple bolts. Call lightning() three times with different x-starting positions. You'll know it worked when three separate bolts appear.

3. Change the bolt color to white. Change monty.pencolor('yellow') to monty.pencolor('white'). You'll know it worked when the bolt looks like a real storm photo.

4. Increase displacement. Change 0.3 to 0.6. You'll know it worked when the bolt has wider, more dramatic bends.

Electrifying!

You used recursive displacement to simulate lightning — the same algorithm used in computer game terrain generation and movie visual effects! Up next: Galaxy Spiral Arms — Archimedean and logarithmic spirals with dot clouds.