# Randomness without Effect

The solution to our problem is to separate describing how we'll use random numbers from the process of actually generating them. This sounds complicated, but it's exactly what we've be doing with `Image` throughout this book. We

• describe an `Image` using paths and methods like `beside`, `above`, and `on`; and
• we only draw an `Image` when we call `draw`.

We do the same thing with Doodle's `Random` type. To access this code we first need to import the `doodle.random` package.

``import doodle.random._``

Now we can create values that describe creating a random number

``````val randomDouble = Random.double
// randomDouble: Free[[A >: Nothing <: Any] => RandomOp[A], Double] = Suspend(
//   a = RDouble
// )``````

No random numbers are actually created until we call the `run` method.

``````randomDouble.run
// res0: Double = 0.5065032285545146``````

The type `Random[Double]` indicates we have something that will produce a random `Double` when we `run` it. Just like with `Image` and `draw`, substitution holds with `Random` up until the point we call `run`.

Table Table generative:random shows some of the ways to construct `Random` values.

Method Description Example -------------------------- ------------------------------ ------------------------------ `Random.always(value)` Creates a `Random` that `Random.always(10)` always produces the given value.

`Random.double` Creates a `Random` that `Random.double` generates a `Double` uniformly distributed between `0.0` and `1.0`.

`Random.int` Creates a `Random` that `Random.int` generates an `Int` uniformly distributed across the entire range.

`Random.natural(limit)` Creates a `Random` that `Random.natural(10)` generates a `Int` uniformly distributed in the range greater than or equal to `0` and less than `1`.

`Random.oneOf(value, ...)` Creates a `Random` that `Random.oneOf("A", "B", "C")` generates one of the given values with equal chance. ----------------------------------------------------------------------------------------

: Some of the methods to create `Random` values. Table generative:random

### Composing Random

Now we've seen how to create a `Random`, how do we compose them into more interesting programs? For example, how could we turn a random `Double` into a random `Angle`? It might be tempting to call `run` every time we want to manipulate a random result, but this will break substitution and is exactly what we're trying to avoid.

Remember when we talked about `map` in the previous chapter we said it transforms the elements but keeps the structure (number of elements) in the `List`. The same analogy applies to the `map` method on `Random`. It lets us transform the element of a `Random`---the value it produces when it is run---but doesn't let us change the structure. Here the "structure" means introducing more randomness, or making a random choice.

We can create a random value and apply a deterministic transformation to it using `map`, but we can't create a random value and them use that value as input to a process that creates another random value.

Here's how we can create a random angle.

``````val randomAngle: Random[Angle] =
Random.double.map(x => x.turns)``````

When we `run` `RandomAngle` we can generate randomly created `Angle`

``````randomAngle.run
// res1: Angle = Angle(4.2275285028507685)
randomAngle.run
// res2: Angle = Angle(3.452938222204342)``````

### Exercises {-}

#### Random Colors {-}

Given `randomAngle` above, create a method that accepts saturation and lightness and generates a random color. Your method should have the signature

``````def randomColor(s: Normalized, l: Normalized): Random[Color] =
???``````

<div class="example"> This is a deterministic transformation of the output of `randomAngle`, so we can implement it using `map`.

``````def randomColor(s: Double, l: Double): Random[Color] =
randomAngle.map(hue => Color.hsl(hue, s, l))``````

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#### Random Circles {-}

Write a method that accepts a radius and a `Random[Color]`, and produces a circle of the given radius and filled with the given random color. It should have the signature

``````def randomCircle(r: Double, color: Random[Color]): Random[Image] =
???``````

<div class="example"> Once again this is a deterministic transformation of the random color, so we can use `map`.

``````def randomCircle(r: Double, color: Random[Color]): Random[Image] =
color.map(fill => Image.circle(r).fillColor(fill))``````

</div>