Coral Branch

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

• Write a recursive function where each call spawns a random number of new calls
• Vary branch angles randomly with random.uniform(-40, 40)
• Shift colors from dark red at the base to pale pink at the tips using depth

A single dark red trunk rises from the sea floor and bursts into a fan of branches — some nodes sprout one branch, some two, some three — ending in a cloud of pale pink tips. This is recursion like the Fractal Tree, but with nature's randomness mixed in.

Welcome to the Coral Reef!

Real coral never branches perfectly evenly — every fork is a little different. In this lab your recursive function will roll the dice at every branch, just like coral growing in the ocean!

How It Works

The branch function draws one segment, then calls random.randint(1, 3) to decide how many sub-branches to spawn — this is called variable-arity recursion because the number of recursive calls varies. Each child turns a random amount between -40° and +40° and is a bit shorter than its parent. The depth parameter counts how many levels deep we are, and it picks both the pen size (thick at the base, thin at the tips) and the color from a dark-red-to-pink list.

Sample Code

import turtle
import random
random.seed(8)

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

colors = ['darkred', 'firebrick', 'crimson', 'palevioletred', 'hotpink', 'lightpink', 'pink', 'mistyrose']

def branch(x, y, heading, length, depth):
    if depth >= 8 or length < 3:
        return
    monty.penup()
    monty.goto(x, y)
    monty.setheading(heading)
    monty.pensize(8 - depth)
    monty.pencolor(colors[depth])
    monty.pendown()
    monty.forward(length)
    nx = monty.xcor()
    ny = monty.ycor()
    kids = random.randint(1, 3)
    for k in range(kids):
        turn = random.uniform(-40, 40)
        branch(nx, ny, heading + turn, length * 0.72, depth + 1)

branch(0, -185, 90, 95, 0)

What Do You Think Will Happen?

This program is full of random choices, but it starts with random.seed(8). If you click Run twice in a row, will you get the same coral both times or a different one each time? Make your guess, then run it twice to check!

Try It Now

▶ Run ↻ Reset

The same coral, every time — random.seed(8) restarts the random-number generator at the exact same spot, so every "random" choice repeats. Were you right?

How It Works

Compare this to the Fractal Tree, where every branch always splits into exactly 2 children at fixed angles. Here kids = random.randint(1, 3) makes the arity (number of recursive calls) random: a node with 1 child makes a long straggly arm, while a node with 3 children makes a dense fan. The color gradient is driven entirely by depth: at depth 0 the trunk uses colors[0] ('darkred'), and each level deeper moves one step along the list toward 'mistyrose'. Pen size does the same trick in reverse with 8 - depth, so the coral is thick where it's dark and delicate where it's pale.

Explanation Table

Line	What it does
kids = random.randint(1, 3)	Each node spawns 1, 2, or 3 sub-branches — variable-arity recursion
turn = random.uniform(-40, 40)	Each child bends a random amount within ±40°
monty.pencolor(colors[depth])	Deeper levels use lighter colors: dark red base, pink tips
if depth >= 8 or length < 3:	The base case — stops the recursion so it can't go on forever

Learning Check

Your Turn — Grow a Fuller Coral

In the program below, random.randint(1, 3) has been changed to random.randint(2, 3), so every node spawns at least two sub-branches. Will this coral be fuller or scrawnier than before? Predict, then run it!

▶ Run ↻ Reset

Much fuller — guaranteeing at least 2 children at every node roughly doubles the branches at each level, so the pink canopy becomes a dense cloud.

Experiments

1. Roll new dice. Change random.seed(8) to another number and run a few times. You'll know it worked when each seed grows its own unique coral.

2. Calm the water. Change random.uniform(-40, 40) to random.uniform(-15, 15). You'll know it worked when the coral grows straighter and more tree-like instead of sprawling sideways.

3. Stretch the branches. Change length * 0.72 to length * 0.78. You'll know it worked when the coral grows taller and lankier, reaching higher up the canvas.

4. Make a sun coral. Replace the color list with ['darkorange', 'orange', 'gold', 'yellow', 'khaki', 'lightyellow', 'ivory', 'white']. You'll know it worked when the coral glows orange at the base and white at the tips.

A Reef of Your Own!

Recursion plus randomness equals life-like shapes — you just proved it! Every seed value is a different coral waiting to be discovered. Up next: Leaf Venation — draw a leaf and give it a realistic skeleton of veins, three levels deep.