creative exercise 1

main.typ

@@ -15,7 +15,7 @@ Collection of solutions to programming exercises as part of Introduction to Prog
 )
 
 #{
-  let count = 10;
+  let count = 11;
   for week in range(1, count + 1).filter(it => it != 8) {
     let a = "./week" + str(week) + "/doc.typ"
     include a

week11/Chaos.java

@@ -0,0 +1,40 @@
+import common.StdDraw;
+
+class Chaos {
+    public static void main(String[] args) {
+        var x = 0.01;
+        var r = Double.parseDouble(args[0]);
+        var buffer = new double[200];
+        buffer[0] = x;
+        StdDraw.enableDoubleBuffering();
+
+        var t = 0;
+        while(true) {
+            System.out.format("t = %3d; x = %s\n", t, x);
+            x = Math.clamp(nextGeneration(x, r), 0, 1);
+
+            var offset = t % buffer.length;
+            if(offset == 0) {
+                StdDraw.clear();
+                buffer = new double[200];
+            }
+            buffer[offset] = x;
+            for(var toDraw = 0; toDraw < buffer.length; toDraw++) {
+                var to = buffer[toDraw];
+                StdDraw.line(toDraw / (double)buffer.length, 0, toDraw / (double) buffer.length, to);
+            }
+            if(offset % 10 == 0) {
+                StdDraw.show();
+                StdDraw.pause(100);
+            }
+            if(offset >= 1 && buffer[offset] == buffer[offset - 1]) { // stabilized value
+                StdDraw.pause(5000);
+            }
+            t += 1;
+        }
+    }
+
+    static double nextGeneration(double x, double r) {
+        return r * x * (1 - x);
+    }
+}

week11/common

@@ -0,0 +1 @@
+../common

week11/doc.typ

@@ -0,0 +1,40 @@
+#import "./common/common.typ" : *
+
+#show: template
+
+= Week 10
+
+== Exercise 1.3.45
+
+_Chaos_. Write a program to study the following simple model for population growth, which might be applied to study fish in a pond, bacteria in a test tube,
+or any of a host of similar situations. We suppose that the population ranges from
+$0$ (extinct) to $1$ (maximum population that can be sustained). If the population at
+time $t$ is $x$, then we suppose the population at time $t + 1$ to be $r x (1-x)$, where the
+argument r, known as the _fecundity parameter_, controls the rate of growth. Start
+with a small population—say, $x = 0.01$—and study the result of iterating the model, for various values of $r$. For which values of $r$ does the population stabilize at
+$x = 1 - 1/r$ ? Can you say anything about the population when $r$ is $3.5$? $3.8$? $5$?
+
+#table(
+  columns: 3,
+  $3.5$,
+  $3.8$,
+  $5$,
+  $2$,
+  [Oscillation between 4 values],
+  [Sustained chaos],
+  [Dies from overpopulation in 5 ticks],
+  [Sustained $1-1/r$]
+)
+
+== Exercise 1.4.26
+
+_Music shuffling_. You set your music player to shuffle mode. It plays each of
+the n songs before repeating any. Write a program to estimate the likelihood that
+you will not hear any sequential pair of songs (that is, song 3 does not follow song
+2, song 10 does not follow song 9, and so on).
+
+== Exercise 1.5.32
+
+_Clock_. Write a program that displays an animation of the second, minute,
+and hour hands of an analog clock. Use the method `StdDraw.pause(1000)` to
+update the display roughly once per second.