diff --git a/exam/ex13/backend.py b/exam/ex13/backend.py
new file mode 100644
index 0000000..283e74d
--- /dev/null
+++ b/exam/ex13/backend.py
@@ -0,0 +1,64 @@
+import numpy as np
+
+CELL_IS_ALIVE = 0b1
+CELL_WILL_BE_ALIVE = 0b10
+CELL_WILL_BE_DEAD = 0b100
+
+def is_alive(model, i, j):
+	return model[i][j] & CELL_IS_ALIVE
+
+def get_cells_around(model, i, j):
+	# Most common case. Handle this first. 
+	# Fortunately the most common case is also the fastets to handle.
+	if(i > 2 and j > 2 and i < model.shape[0] and j < model.shape[1]):
+		return model[i - 2: i + 2, j - 2: j + 2]
+
+	# Neither negative indices nor indices that overflow 
+	# are handled properly by numpy. So basically I have to do that manually:
+	cells_around = np.zeros([3, 3], np.int8)
+	for k, m in enumerate(range(i - 1, i + 2)):
+		for l, n in enumerate(range(j - 1, j + 2)):
+			real_m = m
+			if(m >= model.shape[0]):
+				real_m = m - model.shape[0]
+			if(m < 0):
+				real_m = m + model.shape[0]
+			real_n = n
+			if(n >= model.shape[1]):
+				real_n = n - model.shape[1]
+			if(n < 0):
+				real_n = n + model.shape[1]
+			cells_around[k][l] = model[real_m][real_n]
+	return cells_around
+
+def count_living_cells_around(model, i, j):
+	cells_around = get_cells_around(model, i, j)
+	living_cells_around = (cells_around & CELL_IS_ALIVE) == 1
+	living_cells_around[1][1] = False
+	_, counts = np.unique(living_cells_around, return_counts=True)
+	print(counts)
+	return counts[True]
+
+
+
+def handle_cell(model, i, j):
+	living_cells_around = count_living_cells_around(model, i, j)
+	if(not is_alive(model, i, j)):
+		if(living_cells_around == 3):
+			model[i][j] = CELL_WILL_BE_ALIVE
+		return
+
+	if(living_cells_around > 3 or living_cells_around < 2):
+		model[i][j] = CELL_WILL_BE_DEAD
+
+def after_tick_finished(model):
+	# kill the cells that have died
+	model[(model & CELL_WILL_BE_DEAD) != 0] = 0
+
+	# create the new cells
+	model[(model & CELL_WILL_BE_ALIVE) != 0] = 1
+
+def total_living_cells(model):
+	living_cells = (model & CELL_IS_ALIVE) == 1
+	_, counts = np.unique(living_cells, return_counts=True)
+	return counts[True]
diff --git a/exam/ex13/executor.py b/exam/ex13/executor.py
new file mode 100644
index 0000000..287d53c
--- /dev/null
+++ b/exam/ex13/executor.py
@@ -0,0 +1,11 @@
+from backend import handle_cell, after_tick_finished
+
+def execute_tick(model):
+	n, m = model.shape
+
+	for i in range(n):
+		for j in range(m):
+			handle_cell(model, i, j)
+	after_tick_finished(model)
+
+
diff --git a/exam/ex13/main.py b/exam/ex13/main.py
new file mode 100644
index 0000000..bb56ed6
--- /dev/null
+++ b/exam/ex13/main.py
@@ -0,0 +1,25 @@
+import matplotlib.pyplot as plt
+import numpy as np
+
+from model import prepare_model
+from backend import total_living_cells
+from executor import execute_tick
+
+def cells_alive_at_ticks(model, ticks):
+	for i in range(ticks):
+		execute_tick(model)
+		cell_count = total_living_cells(model)
+		yield i, cell_count
+
+plot_data = {
+	0.3 : ("r", "p=0.3")
+	, 0.5: ("g", "p=0.5")
+	, 0.7: ("b", "p=0.7")
+}
+
+for p, (color, label) in plot_data.items():
+	model = prepare_model(100, p)
+	living_cells = np.array(list(cells_alive_at_ticks(model, 1000)))
+	plt.plot(living_cells[:, 0], living_cells[:, 1], color, label=label)
+
+plt.show()
diff --git a/exam/ex13/model.py b/exam/ex13/model.py
new file mode 100644
index 0000000..80ebc84
--- /dev/null
+++ b/exam/ex13/model.py
@@ -0,0 +1,13 @@
+import numpy as np
+
+def prepare_model(n, p):
+	"""
+	p must be between 0 and 1.
+	"""
+
+	return (np.random.rand(n, n) < p).astype(np.int8)
+
+
+
+
+