Xcode 8 and Swift 3 was released on September 13th, 2016. Please make sure to update as soon as possible. The first lesson has been updated with instructions for checking your version and updating if necessary.

These are the instructions for Xcode 8. If you have Xcode 7 and cannot update, please go back to the dashboard and select the Xcode 7 version.

Let's put all of our knowledge to the test and program some fish artificial intelligence!

When we're finished, we'll have something like this!

Final flocking fish

What are boids?

"Boid" is short for "bird-oid object" or "bird-like object". Its origin goes back to a research paper published in the 80s by that described the concepts we'll be discussing today.

A boid is a member of a simulation that only uses the information it has to navigate the world. Each individual fish will use information about its neighbors and environment to stay close to other fish, avoid colliding with them, and try to move in the same direction.

These simple rules make the artificial intelligence of a single fish very simple. Complex flocking or schooling behavior comes from introducing multiple fish using the same or similar rules.

These basic concepts have been used to simulate groups animals, crowds, and even social networks. Boids are useful for any system that is the combination of many "independent actors" (fish are our "actors").

Math & physics review

Before we move any further, let's make sure we are on the same page with some math concepts you'll need for this project. Some of these are simple, but make sure to read everything so you don't end up missing something important!


The sum of elements is every element added together.

If we had an array of [1, 2, 3, 4], then it's sum would be 1 + 2 + 3 + 4 or 10.


The average of elements is the sum of the elements divided by the total number of elements.

If we had an array of [1, 2, 3, 4], then it's sum would be (1 + 2 + 3 + 4) / 4 or 2.5.


Cartesian points

When working in two-dimensional space, we represent position with a "point" or combination of x and y values. These points are an offset from the "origin" (the bottom left in our case). x values increase to the right and y values increase upwards.

To represent something 5 units to the right of the origin, we would say it has a position of (5, 0). To represent something 5 units to the right and 2 units up, we would say it has a position of (5, 2).

When programming for iOS, we usually use the CGPoint data type to represent positions and other two-dimensional values. Here are some common operations you need for CGPoints. There are a few more that we'll tell you about throughout the tutorial!

Creating a CGPoint

let myPoint: CGPoint = CGPoint(x: 5, y: 2)

Accessing the x or y values

let xValue: CGFloat = myPoint.x
let yValue: CGFloat = myPoint.y

Adding two points together

let myOtherPoint: CGPoint = CGPoint(x: 1, y: 1)
let myNewPoint: CGPoint = myPoint + myOtherPoint
// myNewPoint now contains (6, 3)

Woah, what's a CGFloat?

CGFloat is a special type for decimal values we use when working with graphics on iOS. The "CG" in CGPoint and CGFloat stands for "Core Graphics", a framework used for displaying things on the screen.

While you can create a CGPoint with Int, Double, or CGFloat values, they are always converted to CGFloats. This means our x and y values will always be CGFloats. The biggest issue is arithmetic operations can only be performed between a CGFloat and another CGFloat. There is a single line in this project where it will matter (you'll need to "convert" an Int to a CGFloat). Don't worry, we'll remind you!


The speed of an element is how far it moves in a given period of time.

When an element has a speed of 10 units per second, does that mean that after two seconds of travel it is 20 units away from where it started?

Not necessarily! We do not have enough information to know for sure... If the element moved forward for one second and then backwards for one second then it would end up in the exact same spot!


Velocity is speed with a direction. It solves the "not enough information" problem of speed.

When an element has a velocity of 10 units per second in the positive x direction we know for certain that after two seconds of travel, that element is 20 units to the right of where it started!


A vector is a direction with a magnitude. This means it represents both direction and a value which makes it perfect for representing velocity!

Just like points in two-dimensions, vectors in two-dimensions are represented as a combination of x and y values. For our use case, a vector is just a fancy point. To represent something moving 10 units to the right and 20 units down, we would say it has a velocity of (10, -20).

Each of our fish will have a velocity that determines its new position every calculation. A fish will update its velocity to change its direction.

Vectors are also used to represent how to move from one point to another.

Since vectors are so similar to points, we'll be using CGPoint to store their data. In addition to the things described above, you'll need to know how to do the following...

Scaling a vector

Vectors can be scaled or stretched. When you have a velocity and need to increase it to 3 times its original value, you "scale" it.

let myVector: CGPoint = CGPoint(x: 2, y: 3)
let myScaledVector: CGPoint = myVector * 3
// myScaledVector now contains (6, 9)

You could also do the opposite and decrease its value by scaling by a number less than one.

Reversing a vector

The direction of a vector can be reversed by scaling it by -1.

let myReversedVector: CGPoint = myVector * -1
// myReversedVector now contains (-2, -3)

Vector between two points

To get a vector from one point to another, we subtract the origin from the destination.

let originPoint: CGPoint = CGPoint(x: 1, y: 3)
let destinationPoint: CGPoint = CGPoint(x: 10, y: 10)
let vectorFromOrigin: CGPoint = destinationPoint - originPoint

Sum of [CGPoint]

Let's start applying that math review!

  1. Download the starter project from here.
  2. Double-click the downloaded zip file to "extract it".
  3. Drag this newly extracted folder into your "Make School Projects" folder.
  4. Open your "Make School Projects" folder and double-click MakeSchoolOfFish.xcodeproj and single-click Fish.swift in the left-side navigation to get started!

Towards the bottom of Fish.swift you should see a function called sum. This function takes in an array of CGPoint and is expected to return the sum of all points. Lucky for us, CGPoint values can be added directly to each other.

Fill in the body for sum(of points: [CGPoint]) -> CGPoint. If there are no elements in the points array, it should return CGPoint(x: 0, y: 0). If there are elements, it should iterate over each to calculate and return the sum.

Average of [CGPoint]

Find the average function (it should be below sum). This function will take in an array of CGPoint and is expected to return the average value. Averages for points work the same as averages for numbers expect there is a x-value and y-value that both get averaged! Lucky for us, CGPoint can be added together and divided by a CGFloat.

This is the one place you'll need to convert an Int to a CGFloat. You can do this with CGFloat(myIntValue) where myIntValue is the value you need to convert.

Fill in the body for average(of points: [CGPoint]) -> CGPoint. If there are no elements in the points array, it should return CGPoint(x: 0, y: 0). If there are elements, it should calculate the average using the sum function you just created.

Remember to manually return CGPoint(x: 0, y: 0) if there are no elements in the array. If you do not and average is called with an empty points array, then your code will crash for trying to divide by zero!

Vector to a CGPoint

Find the vectorTo method (it should be the last method in the Fish class). This function takes in a CGPoint and is expected to return the vector from self.position to that point.

Fill in the body for vectorTo(point: CGPoint) -> CGPoint. It should return the vector from self.position to point. See the math review above if you need help with this!

The position instance variable is inherited from SKSpriteNode. SKSpriteNode is part of Sprite Kit -- Apple's game engine. We are using Sprite Kit to display this simulation so we have directly subclasses SKSpriteNode for each fish on the screen.

Vector to center of [CGPoint]

One last math helper! Find the vectorToCenterPoint method (it should be above vectorTo). This function takes in an array of CGPoint and is expected to return the vector from self.position to the average point of that array.

Fill in the body for vectorToCenterPoint(of points: [CGPoint]) -> CGPoint. If there are no elements in the points array, it should return CGPoint(x: 0, y: 0) -- you must do this manually! If there are elements, it should calculate the average using the average function you just created and return the vector to that average point using the vectorTo function you just created.


If you have feedback on this tutorial or find any mistakes, please open issues on the GitHub Repository or comment below.

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