Inward Collapsing Spiral

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

• Create a spiral that converges to a point by decreasing the step length each iteration
• Color segments from bright blue at the outside to white at the center using a fade list
• Understand the difference between increasing sequences (outward) and decreasing sequences (inward)

Instead of growing outward, this spiral collapses inward — starting wide and converging to a near-invisible point at the center. Segments fade from deep blue on the outside to near-white as the spiral tightens to a point.

Welcome to the Inward Spiral!

All the spirals so far grew outward. Now we run the same idea in reverse — start big and shrink toward zero. Let's code it together!

How It Works

The step starts large (at 200) and decreases by a small amount each iteration. When step reaches 0 the path has converged to a point. A color list fades from dark blue through lighter shades to near-white, so the outer segments look bolder and the inner ones fade away.

Sample Code

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

colors = ['midnightblue', 'navy', 'blue', 'royalblue',
          'cornflowerblue', 'lightskyblue', 'lightcyan', 'white']
step = 200

i = 0
while step > 1:
    monty.color(colors[min(i // 25, len(colors) - 1)])
    monty.forward(step)
    monty.right(91)
    step -= 1
    i += 1

What Do You Think Will Happen?

The step starts at 200 and decreases by 1 each iteration. The loop uses right(91) — slightly more than 90°. Will the spiral wind clockwise or counterclockwise? Make your guess — then click Run to find out!

Try It Now

▶ Run ↻ Reset

The spiral winds clockwise because right() turns clockwise. The 91° angle — just 1° past a right angle — makes the path drift slightly so the loops don't overlap exactly. Were you right?

How It Works

while step > 1 runs until the step becomes too small to matter. Each iteration step -= 1 shrinks the path segment — opposite of step += n in the outward spirals.

min(i // 25, len(colors) - 1) maps iteration index to a color but clamps it so we never go past the last color in the list, even if the loop runs longer than expected.

Explanation Table

Line	What it does
step = 200	Start with a long segment
while step > 1	Keep going until segments are tiny
step -= 1	Shrink by 1 pixel each step — creates the inward spiral
right(91)	Slightly more than 90° — prevents loops from sitting exactly on top of each other
min(i // 25, len(colors) - 1)	Advance color every 25 steps, clamped at the list end

Learning Check

Your Turn — Change the Convergence Rate

The spiral currently decreases by 1 per step. Change step -= 1 to step -= 2. Predict how the spiral will change — then run it to see if you were right!

▶ Run ↻ Reset

With step -= 2 the spiral converges twice as fast — it reaches the center in half the steps, so there are fewer revolutions and the loops are spaced further apart.

Experiments

1. Try right(89). One degree less than 90° winds the spiral in the opposite rotational direction. You'll know it worked when the loops tilt the other way.

2. Start even larger. Change step = 200 to step = 300. More revolutions fit before convergence. You'll know it worked when the spiral takes up more of the canvas.

3. Use warm colors. Replace the blues with ['darkred', 'red', 'orangered', 'orange', 'gold', 'yellow', 'lightyellow', 'white']. You'll know it worked when the spiral shifts from deep red to pale yellow.

4. Make it hexagonal. Change right(91) to right(61). You'll know it worked when the corners look more rounded.

Brilliant!

You saw the same spiral rule work in both directions — outward AND inward — just by switching += to -=. Convergence is just divergence in reverse! Up next: Colored Logarithmic Spiral — using trigonometry to draw a truly curved spiral.