2016 Update

Task/Percolation-Mean-run-density/Go/percolation-mean-run-density.go

@@ -0,0 +1,35 @@
+package main
+
+import (
+    "fmt"
+    "math/rand"
+)
+
+var (
+    pList = []float64{.1, .3, .5, .7, .9}
+    nList = []int{1e2, 1e3, 1e4, 1e5}
+    t     = 100
+)
+
+func main() {
+    for _, p := range pList {
+        theory := p * (1 - p)
+        fmt.Printf("\np: %.4f  theory: %.4f  t: %d\n", p, theory, t)
+        fmt.Println("        n          sim     sim-theory")
+        for _, n := range nList {
+            sum := 0
+            for i := 0; i < t; i++ {
+                run := false
+                for j := 0; j < n; j++ {
+                    one := rand.Float64() < p
+                    if one && !run {
+                        sum++
+                    }
+                    run = one
+                }
+            }
+            K := float64(sum) / float64(t) / float64(n)
+            fmt.Printf("%9d %15.4f %9.6f\n", n, K, K-theory)
+        }
+    }
+}

Task/Percolation-Mean-run-density/J/percolation-mean-run-density.j

@@ -1,6 +1,6 @@
 NB. translation of python
 
-NB.  'N P T' =: 100 0.5 500            NB. silliness
+NB.  'N P T' =: 100 0.5 500            NB. hypothetical example values, to aid comprehension...
 
 newv =: (> ?@(#&0))~                   NB. generate a random binary vector.  Use:  N newv P
 runs =: {: + [: +/ 1 0&E.              NB. add the tail to the sum of 1 0 occurrences  Use: runs V

Task/Percolation-Mean-run-density/Mathematica/percolation-mean-run-density.math

@@ -0,0 +1,9 @@
+meanRunDensity[p_, len_, trials_] :=
+ Mean[Length[Cases[Split@#, {1, ___}]] & /@
+    Unitize[Chop[RandomReal[1, {trials, len}], 1 - p]]]/len
+
+Column@Table[
+  Grid[Join[{{p, n, K, diff}},
+    Table[{q, n, x = meanRunDensity[q, n, 100] // N,
+      q (1 - q) - x}, {n, {100, 1000, 10000, 100000}}], {}],
+   Alignment -> Left], {q, {.1, .3, .5, .7, .9}}]

Task/Percolation-Mean-run-density/Pascal/percolation-mean-run-density.pascal

@@ -0,0 +1,52 @@
+{$MODE objFPC}//for using result,parameter runs becomes for variable..
+uses
+  sysutils;//Format
+const
+  MaxN = 100*1000;
+
+function run_test(p:double;len,runs: NativeInt):double;
+var
+   x, y, i,cnt : NativeInt;
+Begin
+  result := 1/ (runs * len);
+  cnt := 0;
+  for  runs := runs-1 downto 0 do
+  Begin
+    x := 0;
+    y := 0;
+    for i := len-1 downto 0 do
+    begin
+      x := y;
+      y := Ord(Random() < p);
+      cnt := cnt+ord(x < y);
+    end;
+  end;
+  result := result *cnt;
+end;
+
+//main
+var
+  p, p1p, K : double;
+  ip, n : nativeInt;
+Begin
+  randomize;
+  writeln( 'running 1000 tests each:'#13#10,
+    ' p      n      K     p(1-p)   diff'#13#10,
+    '-----------------------------------------------');
+  ip:= 1;
+  while ip < 10 do
+  Begin
+     p := ip / 10;
+     p1p := p * (1 - p);
+     n := 100;
+     While n <= MaxN do
+     Begin
+       K := run_test(p, n, 1000);
+       writeln(Format('%4.1f %6d  %6.4f  %6.4f %7.4f (%5.2f %%)',
+         [p, n, K, p1p, K - p1p, (K - p1p) / p1p * 100]));
+       n := n*10;
+     end;
+     writeln;
+     ip := ip+2;
+   end;
+end.