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```# Chaotic Function Analysis Graph
# GrX = Xn
# GrY = Xn+1
# FB - 201012094
import math
import random
from PIL import Image
imgx = 800
imgy = 600
image = Image.new("RGB", (imgx, imgy))
# drawing region
xa = 0.0
xb = 1.0
ya = 0.0
yb = 1.0

x0 = random.random() # initial x does not matter for this type of graph
x1 = x0 # prev x
x2 = x1 # prev of prev x

maxIt = 100000

for i in range(maxIt):
x2 = x1
x1 = x0

# chaotic function to graph
# x0 = math.fmod(math.fabs(math.sin(3.0 * x1 + 0.3)), 1.0) # (0)
# x0 = math.fmod((x1 + math.pi) ** 2.0, 1.0)             # (1)
# x0 = math.fmod((x1 + x2 + math.pi) ** 2.0, 1.0)        # (2) PRNG?
x0 = 4.0 * x1 * (1.0 - x1) # (3) logistic equation in chaotic state
# x0 = (x2 + 3.0) * x1 * (1.0 - x1) # (4) ?

xi = int((imgx - 1) * (x1 - xa) / (xb - xa))
yi = int((imgy - 1) * (x0 - ya) / (yb - ya))
if xi >=0 and xi < imgx and yi >= 0 and yi < imgy:
image.putpixel((xi, yi), (255, 255, 255))

image.save("chaotic_function_graph.png", "PNG")
```

#### Diff to Previous Revision

```--- revision 1 2010-12-09 06:53:53
+++ revision 2 2010-12-10 03:31:50
@@ -1,7 +1,7 @@
# Chaotic Function Analysis Graph
# GrX = Xn
# GrY = Xn+1
-# FB - 201012046
+# FB - 201012094
import math
import random
from PIL import Image
@@ -15,7 +15,7 @@
yb = 1.0

x0 = random.random() # initial x does not matter for this type of graph
-x1 = x # prev x
+x1 = x0 # prev x
x2 = x1 # prev of prev x

maxIt = 100000
@@ -25,9 +25,11 @@
x1 = x0

# chaotic function to graph
-    x0 = math.fmod(math.fabs(math.sin(3.0 * x1 + 0.3)), 1.0) # (0)
+    # x0 = math.fmod(math.fabs(math.sin(3.0 * x1 + 0.3)), 1.0) # (0)
# x0 = math.fmod((x1 + math.pi) ** 2.0, 1.0)             # (1)
# x0 = math.fmod((x1 + x2 + math.pi) ** 2.0, 1.0)        # (2) PRNG?
+    x0 = 4.0 * x1 * (1.0 - x1) # (3) logistic equation in chaotic state
+    # x0 = (x2 + 3.0) * x1 * (1.0 - x1) # (4) ?

xi = int((imgx - 1) * (x1 - xa) / (xb - xa))
yi = int((imgy - 1) * (x0 - ya) / (yb - ya))
```