diff --git a/tests/test_distances.py b/tests/test_distances.py
new file mode 100644
index 0000000..e03cc56
--- /dev/null
+++ b/tests/test_distances.py
@@ -0,0 +1,89 @@
+import pytest
+import taichi as ti
+import taichi.math as tm
+from catsim.tools import (
+    euclidean_distance,
+    manhattan_distance,
+    chebyshev_distance,
+    get_distance,
+)
+from catsim.constants import (
+    EUCLIDEAN_DISTANCE,
+    CHEBYSHEV_DISTANCE,
+    MANHATTAN_DISTANCE,
+)
+
+
+@ti.data_oriented
+class TestDistanceFunctions:
+    @ti.kernel
+    def get_euclidean(self, p1: tm.vec2, p2: tm.vec2) -> ti.f32:
+        return euclidean_distance(p1, p2)
+
+    @ti.kernel
+    def get_manhattan(self, p1: tm.vec2, p2: tm.vec2) -> ti.f32:
+        return manhattan_distance(p1, p2)
+
+    @ti.kernel
+    def get_chebyshev(self, p1: tm.vec2, p2: tm.vec2) -> ti.f32:
+        return chebyshev_distance(p1, p2)
+
+    @ti.kernel
+    def get_distance_by_type(
+        self, p1: tm.vec2, p2: tm.vec2, distance_type: ti.i32
+    ) -> ti.f32:
+        return get_distance(p1, p2, distance_type)
+
+    @pytest.mark.parametrize(
+        "p1, p2, expected",
+        [
+            (tm.vec2(0, 0), tm.vec2(3, 4), 5.0),
+            (tm.vec2(1, 1), tm.vec2(4, 5), 5.0),
+            (tm.vec2(-2, -3), tm.vec2(1, 1), 5.0),
+            (tm.vec2(-1.5, 0), tm.vec2(1.0, 0), 2.5),
+            (tm.vec2(-1e5, -1e5), tm.vec2(-1e5, -1e5), 0.0),
+            (tm.vec2(1000, 2000), tm.vec2(3000, 4000), 2828.4271247),
+            (tm.vec2(1e5, 1e5), tm.vec2(-1e4, -1e6), 1105486.3183232),
+        ],
+    )
+    def test_euclidean(self, p1, p2, expected):
+        result = self.get_euclidean(p1, p2)
+        assert pytest.approx(result, 0.001) == expected
+
+    @pytest.mark.parametrize(
+        "p1, p2, expected",
+        [
+            (tm.vec2(0, 0), tm.vec2(3, 4), 7.0),
+            (tm.vec2(-2, -3), tm.vec2(1, 1), 7.0),
+            (tm.vec2(-5, -10), tm.vec2(-6, -3), 8.0),
+            (tm.vec2(-1, -2), tm.vec2(5, -7), 11.0),
+        ],
+    )
+    def test_manhattan(self, p1, p2, expected):
+        result = self.get_manhattan(p1, p2)
+        assert pytest.approx(result, 0.001) == expected
+
+    @pytest.mark.parametrize(
+        "p1, p2, expected",
+        [
+            (tm.vec2(0, 0), tm.vec2(3, 4), 4.0),
+            (tm.vec2(-2, -3), tm.vec2(1, -5), 3.0),
+            (tm.vec2(-2, -3), tm.vec2(1, -7), 4.0),
+            (tm.vec2(-5, -10), tm.vec2(-6, -3), 7.0),
+        ],
+    )
+    def test_chebyshev(self, p1, p2, expected):
+        result = self.get_chebyshev(p1, p2)
+        assert pytest.approx(result, 0.001) == expected
+
+    @pytest.mark.parametrize(
+        "dist_type, p1, p2, expected",
+        [
+            (EUCLIDEAN_DISTANCE, tm.vec2(0, 0), tm.vec2(3, 4), 5.0),
+            (MANHATTAN_DISTANCE, tm.vec2(0, 0), tm.vec2(3, 4), 7.0),
+            (CHEBYSHEV_DISTANCE, tm.vec2(0, 0), tm.vec2(3, 4), 4.0),
+        ],
+    )
+    def test_distance(self, dist_type, p1, p2, expected):
+        result = self.get_distance_by_type(p1, p2, dist_type)
+        assert pytest.approx(result, 0.001) == expected
diff --git a/tests/test_initialization.py b/tests/test_initialization.py
new file mode 100644
index 0000000..f6c459e
--- /dev/null
+++ b/tests/test_initialization.py
@@ -0,0 +1,62 @@
+import taichi as ti
+import catsim.cat as cat
+from catsim.constants import (
+    DISABLE_PROB_INTER,
+    MOVE_PATTERN_RANDOM_ID,
+    MOVE_PATTERN_LINE_ID,
+)
+
+
+def init_cat_env(move_radius, r0, r1, width, height, move_pattern, prob_inter):
+    cat.init_cat_env(
+        move_radius,
+        r0,
+        r1,
+        width,
+        height,
+        move_pattern,
+        prob_inter,
+    )
+
+
+def test_init_cat_env():
+    cat.init_cat_env(
+        move_radius=10.5,
+        r0=2.0,
+        r1=8.0,
+        width=100,
+        height=200,
+        move_pattern=MOVE_PATTERN_RANDOM_ID,
+        prob_inter=DISABLE_PROB_INTER,
+    )
+    assert cat._MOVE_RADIUS == 10.5
+    assert cat._RADIUS_0 == 2.0
+    assert cat._RADIUS_1 == 8.0
+    assert cat._PLATE_WIDTH == 100
+    assert cat._PLATE_HEIGHT == 200
+    assert cat._MOVE_PATTERN == MOVE_PATTERN_RANDOM_ID
+    assert cat._PROB_INTER == DISABLE_PROB_INTER
+
+
+@ti.kernel
+def init_cat(cat_r: ti.f32) -> cat.Cat:
+    catInstance = cat.Cat()
+    catInstance.init_cat(cat_r)
+    return catInstance
+
+
+def test_cat_initialization_with_env():
+    cat.init_cat_env(
+        move_radius=15.0,
+        r0=5.0,
+        r1=10.0,
+        width=50,
+        height=50,
+        move_pattern=MOVE_PATTERN_LINE_ID,
+        prob_inter=DISABLE_PROB_INTER,
+    )
+    catInstance = init_cat(3.0)
+    assert 0 <= catInstance.point[0] <= cat._PLATE_WIDTH
+    assert 0 <= catInstance.point[0] <= cat._PLATE_HEIGHT
+    assert catInstance.radius == 3.0
+    assert catInstance.move_pattern == MOVE_PATTERN_LINE_ID
diff --git a/tests/test_move.py b/tests/test_move.py
index f6e84c4..6581212 100644
--- a/tests/test_move.py
+++ b/tests/test_move.py
@@ -2,7 +2,7 @@
 import taichi as ti
 import taichi.math as tm
 
-from catsim.tools import move_pattern_line, move_pattern_random
+from catsim.tools import move_pattern_line, move_pattern_random, move_pattern_phis
 
 
 @ti.data_oriented
@@ -24,6 +24,12 @@ def move_line(
     ) -> tm.vec2:
         return move_pattern_line(point, old_point, move_r, plate_w, plate_h)
 
+    @ti.kernel
+    def move_phis(
+        self, point: tm.vec2, old_point: tm.vec2, plate_w: ti.i32, plate_h: ti.i32
+    ) -> tm.vec2:
+        return move_pattern_phis(point, old_point, plate_w, plate_h)
+
     @pytest.mark.parametrize(
         "x, y, move_radius",
         [
@@ -58,3 +64,20 @@ def test_move_radius(self, x: int, y: int, move_radius: int):
             new_point[0] - point[0] <= move_radius
             and new_point[1] - point[1] <= move_radius
         )
+
+    @pytest.mark.parametrize(
+        "x, y, old_x, old_y, plate_w, plate_h, expected_x, expected_y",
+        [
+            (10, 10, 5, 5, 100, 100, 15, 15),
+            (0, 0, 10, 10, 100, 100, 10, 10),
+            (5, 5, 20, 20, 30, 30, 15, 15),
+        ],
+    )
+    def test_move_phis(
+        self, x, y, old_x, old_y, plate_w, plate_h, expected_x, expected_y
+    ):
+        point = tm.vec2(x, y)
+        old_point = tm.vec2(old_x, old_y)
+        new_point = self.move_phis(point, old_point, plate_w, plate_h)
+        assert new_point[0] == expected_x
+        assert new_point[1] == expected_y