diff --git a/docs/notebooks/point_clouds.ipynb b/docs/notebooks/point_clouds.ipynb
index ccffa7bf7..7447d8cd6 100644
--- a/docs/notebooks/point_clouds.ipynb
+++ b/docs/notebooks/point_clouds.ipynb
@@ -216989,7 +216989,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 72,
+   "execution_count": 81,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -217000,42 +217000,17 @@
     "    label = (\n",
     "        r\"$T_{x\\rightarrow y}(x)$\" if forward else r\"$T_{y\\rightarrow x}(y)$\"\n",
     "    )\n",
-    "    plt.scatter(*x.T, s=200, edgecolors=\"k\", marker=\"o\", label=r\"$x$\")\n",
-    "    plt.scatter(*y.T, s=200, edgecolors=\"k\", marker=\"X\", label=r\"$y$\")\n",
-    "    plt.scatter(*z.T, s=150, edgecolors=\"k\", marker=marker_t, label=label)\n",
     "    plt.plot(\n",
     "        jnp.vstack((x[:, 0] if forward else y[:, 0], z[:, 0])),\n",
     "        jnp.vstack((x[:, 1] if forward else y[:, 1], z[:, 1])),\n",
     "        c=\"k\",\n",
     "    )\n",
+    "    plt.scatter(*x.T, s=200, edgecolors=\"k\", marker=\"o\", label=r\"$x$\")\n",
+    "    plt.scatter(*y.T, s=200, edgecolors=\"k\", marker=\"X\", label=r\"$y$\")\n",
+    "    plt.scatter(*z.T, s=150, edgecolors=\"k\", marker=marker_t, label=label)\n",
     "    plt.legend(fontsize=22)"
    ]
   },
-  {
-   "cell_type": "code",
-   "execution_count": 73,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "(13, 2)"
-      ]
-     },
-     "execution_count": 73,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "forward = True\n",
-    "z = dual_potentials.transport(x)\n",
-    "p = jnp.stack((x[:, 0] if forward else y[:, 0], z[:, 0]), axis=-1)\n",
-    "q = jnp.stack((x[:, 1] if forward else y[:, 1], z[:, 1]), axis=-1)\n",
-    "p.shape\n",
-    "q.shape"
-   ]
-  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -217045,7 +217020,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 74,
+   "execution_count": 82,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -217056,7 +217031,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 75,
+   "execution_count": 83,
    "metadata": {},
    "outputs": [
     {
@@ -217078,7 +217053,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 76,
+   "execution_count": 84,
    "metadata": {},
    "outputs": [
     {
@@ -217102,12 +217077,12 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "We can also experiment with that method using a more exotic cost function, here a squared `p=1.1` Norm."
+    "We can also experiment with that method using a more exotic cost function that penalizes \"diagonal\" moves (here a squared `p=1.1` Norm.), one gets a different type of map."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 78,
+   "execution_count": 88,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -217118,7 +217093,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 79,
+   "execution_count": 89,
    "metadata": {},
    "outputs": [
     {
@@ -217140,7 +217115,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 80,
+   "execution_count": 90,
    "metadata": {},
    "outputs": [
     {
@@ -217159,13 +217134,6 @@
    "source": [
     "plot_map(x, y, dual_potentials.transport(y, forward=False), forward=False)"
    ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
   }
  ],
  "metadata": {