[Leejohnston]

How to Build a Simple Simulation — Step-by-Step (Beginner Friendly)

Simulations are a huge part of science — physics, biology, chemistry, astronomy, climate science, and even AI. 
This guide shows you how to build a simple simulation in Python from scratch.

No experience needed.

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1. What Is a Simulation?

A simulation is a model that:
• follows rules 
• updates over time 
• calculates new values 
• shows what happens step-by-step 

Examples:
• motion of a falling object 
• bacteria growth 
• population models 
• temperature cooling 
• planetary orbits 

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2. Step 1 — Define the Variables

Every simulation begins with variables.

Example: a falling object

Code:

height = 100    # meters
velocity = 0    # m/s
gravity = -9.8  # m/s^2
dt = 0.1        # time step

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3. Step 2 — Write the Update Rules

Rules describe how the system changes each step.

Physics: 
• velocity changes by gravity 
• height changes by velocity 

Code:

velocity = velocity + gravity * dt
height = height + velocity * dt

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4. Step 3 — Create a Loop

A loop repeats the update rules again and again.

Code:

for step in range(200):
    velocity = velocity + gravity * dt
    height = height + velocity * dt
    print(step, height, velocity)

This prints the height and velocity at every step.

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5. Step 4 — Stop the Simulation Safely

Stop when the object hits the ground:

Code:

if height <= 0:
    height = 0
    break

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6. Full Working Simulation (Copy & Run)

Code:

height = 100
velocity = 0
gravity = -9.8
dt = 0.1

for step in range(1000):
    velocity = velocity + gravity * dt
    height = height + velocity * dt
   
    if height <= 0:
        height = 0
        print("Object hit the ground at step:", step)
        break
       
    print(step, height, velocity)

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7. Step 5 — Plot the Results

Use matplotlib to visualise the height over time:

Code:

import matplotlib.pyplot as plt

heights = []
times = []

height = 100
velocity = 0
gravity = -9.8
dt = 0.1

time = 0

while height > 0:
    velocity += gravity * dt
    height += velocity * dt
   
    heights.append(height)
    times.append(time)
   
    time += dt

plt.plot(times, heights)
plt.xlabel("Time (s)")
plt.ylabel("Height (m)")
plt.title("Object Falling Simulation")
plt.grid(True)
plt.show()

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8. What Can You Simulate Next?

Once you master the template, you can simulate:
• population growth 
• cooling/heating equations 
• radioactive decay 
• predator–prey cycles 
• bouncing balls 
• planetary orbits 
• simple ecosystems 
• particle motion 
• chemical reactions 
• epidemics 

Simulations follow the same pattern:
1. define variables 
2. write update rules 
3. loop over time 
4. record data 
5. plot results 

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9. Common Mistakes

❌ Using too large a time step (dt) 
✔ smaller dt = more accurate simulation 

❌ Forgetting to record results 
✔ store values in lists for plotting 

❌ Mixing floats and ints incorrectly 
✔ always use decimals (e.g., 0.1) 

❌ Not stopping the simulation 
✔ always check for conditions (like hitting the ground) 

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Summary

To build any simulation:
• choose variables 
• define rules 
• update each step 
• repeat in a loop 
• graph the results 

This is how scientists model everything from planets to cells.