Double Helix Spiral

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

• Draw two interleaved spirals from a single loop by alternating between two color assignments
• Understand phase offset — starting two spirals 180° apart so they never overlap
• See how one loop can produce two independent patterns by checking i % 2

Two spirals wind outward together — one red, one blue — offset exactly half a revolution apart. They expand at the same rate so they stay interleaved forever without ever crossing.

Welcome to the Double Helix!

DNA's famous double helix is two strands wound together with a half-turn offset. This lab builds the same idea with turtle graphics — two spirals in one loop! Let's code it together!

How It Works

The key insight: two square spirals that start 180° apart and grow at the same rate will always stay exactly half a revolution apart. We draw them by alternating colors each step using i % 2:

• Even steps (0, 2, 4 …) → red spiral
• Odd steps (1, 3, 5 …) → blue spiral

Because consecutive even steps share the same spiral arm, the two patterns weave together.

Sample Code

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

step = 2

for i in range(400):
    if i % 2 == 0:
        monty.color('crimson')
    else:
        monty.color('royalblue')
    monty.forward(step)
    monty.right(91)
    if i % 2 == 0:
        step += 1

What Do You Think Will Happen?

Step grows only on even iterations (i % 2 == 0). Will the two spirals stay the same size, or will one grow faster than the other? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

They stay the same size — growing at exactly the same rate because step increases on every even step, and both spirals advance by that same step value. Were you right?

How It Works

right(91) — slightly past 90° — makes the path drift so spiral loops don't sit exactly on top of each other. Each loop shifts by 1° per revolution, giving the interleaved arms their visible separation.

step grows only on even iterations, but since odd iterations immediately follow and use the same step, both spirals advance by the same amount. The step only increments once per pair.

Explanation Table

Line	What it does
i % 2 == 0	Selects red on even steps, blue on odd
monty.right(91)	Slightly drifting 90° turn — keeps loops separated
if i % 2 == 0: step += 1	Grow step once per pair of segments
range(400)	400 steps = 200 red + 200 blue segments

Learning Check

Your Turn — Add a Third Spiral

Can you modify the code to draw three interleaved spirals in red, blue, and green? Use i % 3 instead of i % 2 and add a third color condition.

▶ Run ↻ Reset

Using i % 3 selects one of three colors in rotation. The step grows once every three steps — slower than the double helix, so the loops pack slightly tighter.

Experiments

1. Change the drift. Try right(92) or right(89). More drift means loops shift more per revolution. You'll know it worked when the interleaving gaps change size.

2. Increase the step growth. Change step += 1 to step += 2. The spiral expands faster and fewer revolutions fit. You'll know it worked when the arms are spaced further apart.

3. Use complementary colors. Try 'darkorange' and 'dodgerblue' — colors opposite on the color wheel. You'll know it worked when the contrast between arms is even stronger.

4. Draw just one spiral. Remove the color alternation and use a single color. You'll know it worked when the double-strand pattern collapses back to a single spiral.

Double the Fun!

You built two spirals in one loop using a single i % 2 check — the same trick that's used in animation to alternate between two objects every frame! Up next: Fibonacci Spiral — the most famous spiral in nature.