- Arranging items in a line – by width
- Arranging items in a line – by item count
- Geometric Progressions
- Accumulating versus deriving
- Bending the line
- Waves

# Arranging items in a line – by width

This code draws a line of items – as many as necessary to reach the edge of the canvas. In this case, the items are circles. The code can be adapted to draw squares, or more complicated figures composed of multiple shapes.

The code draws shapes as will fit in the canvas width (`x <= width`

), spaced 50 pixels apart (`x += 50`

).

```
function setup() {
createCanvas(windowWidth, windowHeight);
background(100);
}
function draw() {
for (let x = 10; x <= width; x += 50) {
circle(x, 100, 40);
}
}
```

# Arranging items in a line – by item count

What if we want to draw a fixed number of items? This code draws exactly 20 items, no matter how wide the canvas is. It uses `i`

to count the number of shapes, from 0 to 19.

```
function draw() {
let x = 10;
for (let i = 0; i < 20; i++) {
circle(x, 100, 40);
x += 50;
}
}
```

Note: From here on, the definition of `setup()`

is not shown. Each of the following code samples assumes that the sketch also contains a `setup()`

function:

```
function setup() {
createCanvas(windowWidth, windowHeight);
background(100);
}
```

# Geometric Progressions

The code above increases `x`

by the same amount each step. This is an *arithmetic progression*.

We can also increase `x`

by an increasing amount. This is a *geometric progression*.

```
function draw() {
let x = 10;
for (let i = 0; i < 20; i++) {
circle(x, 100, 40);
x *= 1.2;
}
}
```

Changing the spacing is useful when the size changes too.

```
function draw() {
let x = 20;
let size = 5;
for (let i = 0; i < 20; i++) {
circle(x, 100, size);
x *= 1.15;
size *= 1.15;
}
}
```

# Accumulating versus deriving

Back to the arithmetic progression:

```
function draw() {
let x = 10;
for (let i = 10; i < 20; i++) {
circle(x, 100, 40);
x += 50;
}
}
```

This strategy for computing the value of `x`

** accumulates** a value.

`x`

starts out with a value (10); then each time through the loop, the value is updated.An alternative to accumulation is to * derive* the value of

`x`

from scratch each time, directly from the value of `i`

. The *shape position*is derived from the

*loop index*. This has the same effect as the previous code, but it will allow us to plug in different functions besides the linear function $x = 10 + 50i$ used here. We’ll see that later.

```
function draw() {
for (let i = 0; i < 20; i++) {
let x = 10 + 50 * i;
circle(x, 100, 40);
}
}
```

# Bending the line

Derive `y`

from `i`

as well.

```
function draw() {
for (let i = 0; i < 20; i++) {
let x = 10 + 50 * i;
let y = 100 + 10 * i;
circle(x, y, 40);
}
}
```

Replace `10 * i`

by `20 * i`

(left) or `5 * i`

(right) to increase or decrease the *angle* of the line (to make it more or less steep).

# Waves

The payoff to using a function to compute the position is that we can use different functions, for different effects. For example, $y = 100 + 20 \sin(i)$.

`sin()`

returns a number between -1 and 1. Varying the y position by that much is barely detectable. (Try it.) This code multiples the output of `sin()`

by 20, to produce a number between -20 and 20, for a more pronounced wiggle. (It is similar to `random(-20, 20)`

, except that the change from one circle to the next is sinusoidal instead of random.)

```
function draw() {
for (let i = 0; i < 20; i++) {
let x = 10 + 50 * i;
let y = 100 + 20 * sin(i);
circle(x, y, 40);
}
}
```

Instead of using an equation $y = 100 + 20 \sin(i)$, we can use the `map()`

function to do the same thing. Either `y = 100 + map(sin(i), -1, 1, -20, 20)`

or `y = map(sin(i), -1, 1, 80, 120)`

would work. The latter most clearly expresses the range of values (80 to 120) that wil be assigned to `y`

.

```
function draw() {
for (let i = 0; i < 20; i++) {
let x = 10 + 50 * i;
let y = map(sin(i), -1, 1, 80, 120);
circle(x, y, 40);
}
}
```

Also vary the size:

```
function draw() {
for (let i = 0; i < 20; i++) {
let x = 10 + 50 * i;
let y = map(sin(i), -1, 1, 80, 120);
let size = 20 + 20 * cos(i);
circle(x, y, size);
}
}
```

©2020–2022 by Oliver Steele.