diff --git a/logistic.py b/logistic.py
index e49d1c2..7f62337 100644
--- a/logistic.py
+++ b/logistic.py
@@ -1 +1,12 @@
-# Your code goes here
+def f(x, r):
+    """
+    Implements the logistic function.
+    """
+    return r * x * (1 - x)
+
+def iterate_f(x, r, it):
+    traj = [x]
+    for _ in range(it):
+        x = f(x, r)
+        traj.append(x)
+    return traj
diff --git a/logistic_fit.py b/logistic_fit.py
index 1d38ac7..55ee1f0 100644
--- a/logistic_fit.py
+++ b/logistic_fit.py
@@ -24,7 +24,7 @@ def fit_r(xs):
     it = len(xs) - 1
 
     def error(r):
-        return np.linalg.norm(xs - iterate_f(it, x0, r))
+        return np.linalg.norm(xs - iterate_f(x0, r, it))
 
     errors = []
     for r in np.linspace(0, 4, 4001):
diff --git a/test_logistic.py b/test_logistic.py
index 9391bee..e6a4c41 100644
--- a/test_logistic.py
+++ b/test_logistic.py
@@ -1,16 +1,65 @@
+import pytest
+import numpy as np
 from numpy.testing import assert_allclose
-
 from logistic import f
+# from logistic import f, iterate_f
+from logistic_fit import fit_r
+from logistic import iterate_f
 
-# Add here your test for the logistic map
+SEED = np.random.randint(0, 2**31)
 
+@pytest.fixture
+def random_state():
+    print(f'Using seed {SEED}')
+    random_state = np.random.RandomState(SEED)
+    return random_state
 
-def test_f_corner_cases():
-    # Test cases are (x, r, expected)
-    cases = [
+@pytest.mark.parametrize('x, r, expected', [
         (0, 1.1, 0),
         (1, 3.7, 0),
     ]
-    for x, r, expected in cases:
-        result = f(x, r)
-        assert_allclose(result, expected)
+)
+def test_f_corner_cases(x, r, expected):
+    result = f(x, r)
+    assert_allclose(result, expected)
+
+@pytest.mark.parametrize(
+    'x, r, expected',
+    [
+        (0.1, 2.2, 0.198),
+        (0.2, 3.4, 0.544),
+        (0.5, 2, 0.5),
+    ]
+)
+def test_f_generic_cases(x, r, expected):
+    result = f(x, r)
+    assert_allclose(result, expected)
+
+@pytest.mark.parametrize(
+    'x, r, it, expected', 
+    [
+        (0.1, 2.2, 1, [0.1, 0.198]),
+        (0.2, 3.4, 4, [0.2, 0.544, 0.843418, 0.449019, 0.841163]),
+        (0.5, 2, 3, [0.5, 0.5, 0.5, 0.5]),
+    ]
+)
+def test_iterate_f(x, r, it, expected):
+    result = iterate_f(x, r, it)
+    assert_allclose(result, expected, rtol=5e-07)
+
+@pytest.mark.parametrize(
+    'x, r, it',
+    [
+        (0.3, 3.421, 23)
+    ]
+)
+def test_fit_r(x, r, it):
+    traj = iterate_f(x, r, it)
+    r_fitted = fit_r(traj)
+    assert_allclose(r, r_fitted)
+
+def test_random_converge(random_state, r=1.5, it=100, expected=1/3, low=0.0001, high=0.9999):
+    for _ in range(100):
+        x0 = random_state.uniform(low, high)
+        traj = iterate_f(x0, r, it)
+        assert_allclose(traj[-1], expected, atol=1e-3)
\ No newline at end of file