diff --git a/logistic.py b/logistic.py
index e49d1c2..6983207 100644
--- a/logistic.py
+++ b/logistic.py
@@ -1 +1,17 @@
 # Your code goes here
+def f(x,r):
+    return r*x*(1-x)
+
+def iterate_f(x0,r,it):
+    iteration_timecourse = []
+
+    iteration_timecourse.append(x0)
+
+    x = f(x0,r)
+    iteration_timecourse.append(x)
+
+    for i in range(it-1):
+        x = f(x,r)
+        iteration_timecourse.append(x)
+
+    return iteration_timecourse 
\ No newline at end of file
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/plot_logistic.py b/plot_logistic.py
index 6227b5f..03bd185 100644
--- a/plot_logistic.py
+++ b/plot_logistic.py
@@ -10,7 +10,7 @@
 from logistic import iterate_f
 
 
-def plot_trajectory(n, r, x0, fname="single_trajectory.png"):
+def plot_trajectory(x0,r,n, fname="single_trajectory.png"):
     """
     Saves a plot of a single trajectory of the logistic function
 
@@ -23,9 +23,9 @@ def plot_trajectory(n, r, x0, fname="single_trajectory.png"):
     returns
         fig, ax (matplotlib objects)
     """
-    xs = iterate_f(n, x0, r)
+    xs = iterate_f(x0, r, n)
     fig, ax = plt.subplots(figsize=(10, 5))
-    ax.plot(list(range(n)), xs)
+    ax.plot(list(range(n+1)), xs)
     fig.suptitle('Logistic Function')
 
     fig.savefig(fname)
@@ -68,3 +68,14 @@ def plot_bifurcation(start, end, step, fname="bifurcation.png", it=100000,
     ax.set_xlabel("r")
     fig.savefig(fname)
     return fig, ax
+
+
+
+
+
+x0=0.1
+r=1.5
+n=20
+
+plot_trajectory(x0, r, n)
+   
\ No newline at end of file
diff --git a/single_trajectory.png b/single_trajectory.png
new file mode 100644
index 0000000..ae4a274
Binary files /dev/null and b/single_trajectory.png differ
diff --git a/test_logistic.py b/test_logistic.py
index 9391bee..1904ede 100644
--- a/test_logistic.py
+++ b/test_logistic.py
@@ -1,16 +1,60 @@
 from numpy.testing import assert_allclose
+from logistic import f, iterate_f
+import pytest
+from math import isclose
+import numpy as np
 
-from logistic import f
-
+SEED = np.random.randint(0, 2**31)
 # Add here your test for the logistic map
 
+# def test_f_general():
+#     cases = [
+#         (0.1, 2.2, 0.198),
+#         (0.2, 3.4, 0.544),
+#         (0.5, 2, 0.5),
+#     ]
+#     for x, r, expected in cases:
+#         result = f(x, r)
+#         assert_allclose(result, expected)
+
+
+# def test_f_corner_cases():
+#     # Test cases are (x, r, expected)
+#     cases = [
+#         (0, 1.1, 0),
+#         (1, 3.7, 0),
+#     ]
+#     for x, r, expected in cases:
+#         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),(0,1.1,0),(1,3.7,0)])
+# def test_f(x,r,expected):
+#     result = f(x,r)
+#     assert isclose(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,atol=0.001)
+
+@pytest.fixture
+def random_state():
+    print(f'\nUsing Seed: {SEED}')
+    random_state = np.random.RandomState(SEED)
+    return random_state
 
-def test_f_corner_cases():
-    # Test cases are (x, r, expected)
-    cases = [
-        (0, 1.1, 0),
-        (1, 3.7, 0),
-    ]
-    for x, r, expected in cases:
-        result = f(x, r)
-        assert_allclose(result, expected)
+def test_random_starting_point_convergence(random_state):
+    r = 1.5
+    n = 100
+    it = 30
+    n_convergence_datapoints = 3
+    for _ in range(n):
+        x0 = random_state.uniform(0.0001, 0.9999)
+        xs = iterate_f(x0,r,it)
+        for i in range(1, n_convergence_datapoints+1):
+            assert np.isclose(xs[-i], 1/3, atol=0.001)
+        
\ No newline at end of file