Add randomness to the generative art example

Author: noelwelsh

src/pages/indexed-types/conclusions.md

@@ -22,7 +22,7 @@ Also see @duregard12:feat for an approach specialized to enumerating algebraic d
 More recently machine learning techniques are being explored. See, for example, @reddy20:rlcheck and @lemieux23:codamosa.
 @goldstein24:practice studies how property based testing is used in practice.
 
-I mentioned that the probability monad can be used in generative art. Generative art is, broadly, art that is generated by some algorithmic process. This can include an element of randomness. While there are papers on generative art (e.g. [@boden09:generative; @dorin12:generative]), and many other resources that discuss it, it's much more fun to create some yourself. Figure [@fig:indexed-types:cycloid] shows an example of generative art, though this example is not one that uses randomness. The code is below, and it has many knobs that you can play with to create your own example. Just add the `@main` annotation to the `cycloid` method and you can run the code from the Scala CLI. Have fun!
+I mentioned that the probability monad can be used in generative art. Generative art is, broadly, art that is generated by some algorithmic process. This can include an element of randomness. While there are papers on generative art (e.g. [@boden09:generative; @dorin12:generative]), and many other resources that discuss it, it's much more fun to create some yourself. Figure [@fig:indexed-types:cycloid] shows an example of generative art. The code is below, and it has many knobs that you can play with to create your own example. Just add the `@main` annotation to the `cycloid` method and you can run the code from the Scala CLI. Have fun!
 
 ![A set of cycloids showing five-fold symmetry](src/pages/indexed-types/cycloid.pdf){#fig:indexed-types:cycloid}
 
@@ -34,9 +34,10 @@ import cats.syntax.all.*
 import cats.effect.unsafe.implicits.global
 import doodle.core.*
 import doodle.core.format.{Pdf, Png}
+import doodle.interact.syntax.interpolation.*
+import doodle.random.{*, given}
 import doodle.syntax.all.*
 import doodle.java2d.*
-import doodle.interact.syntax.interpolation.*
 
 def cycloid(): Unit = {
   given Monoid[Angle => Vec] with {
@@ -75,6 +76,18 @@ def cycloid(): Unit = {
       .andThen(phase(90.degrees))
       .andThen(radius(0.33 * amplitude)))
 
+  val randomCycloid: Random[Double => Angle => Vec] =
+    for {
+      d <- Random.int(3, 25) // Degree of symmetry
+      n <- Random.natural(d) // Offset from d
+      m1 <- Random.int(1, 5)
+      m2 <- Random.int(m1, m1 + 5)
+    } yield amplitude =>
+      cycloid(n, amplitude) |+| cycloid(
+        m1 * d + n,
+        0.5 * amplitude
+      ) |+| phase(90.degrees).andThen(cycloid(m2 * d + n, 0.33 * amplitude))
+
   def drawCycloid(
       cycloid: Angle => Vec,
       start: Angle = 0.degrees,
@@ -89,16 +102,20 @@ def cycloid(): Unit = {
         .toList
     )
 
-  val picture =
+  /** Repeatedly draw a cycloid with increasing size and a slow turn */
+  def drawCycloids(cycloid: Double => Angle => Vec): Picture[Unit] =
     (0.0)
       .upTo(1.0)
-      .forSteps(50)
+      .forSteps(30)
       .map { m =>
-        drawCycloid(c1(350 * m + 100)).rotate(30.degrees * m)
+        drawCycloid(cycloid(350 * m + 100)).rotate(30.degrees * m)
       }
       .toList
       .allOn
 
+  // val picture = drawCycloids(c1)
+  val picture = randomCycloid.map(drawCycloids).run
+
   val frame = Frame.default
 
   picture.drawWithFrame(frame)