diff --git a/03_classification.ipynb b/03_classification.ipynb
index 6c8c7fc..877ab61 100644
--- a/03_classification.ipynb
+++ b/03_classification.ipynb
@@ -197,16 +197,24 @@
     "def plot_digits(instances, images_per_row=10, **options):\n",
     "    size = 28\n",
     "    images_per_row = min(len(instances), images_per_row)\n",
-    "    images = [instance.reshape(size,size) for instance in instances]\n",
+    "    # This is equivalent to n_rows = ceil(len(instances) / images_per_row):\n",
     "    n_rows = (len(instances) - 1) // images_per_row + 1\n",
-    "    row_images = []\n",
+    "\n",
+    "    # Append empty images to fill the end of the grid, if needed:\n",
     "    n_empty = n_rows * images_per_row - len(instances)\n",
-    "    images.append(np.zeros((size, size * n_empty)))\n",
-    "    for row in range(n_rows):\n",
-    "        rimages = images[row * images_per_row : (row + 1) * images_per_row]\n",
-    "        row_images.append(np.concatenate(rimages, axis=1))\n",
-    "    image = np.concatenate(row_images, axis=0)\n",
-    "    plt.imshow(image, cmap = mpl.cm.binary, **options)\n",
+    "    padded_instances = np.concatenate([instances, np.zeros((n_empty, size * size))], axis=0)\n",
+    "\n",
+    "    # Reshape the array so it's organized as a grid containing 28×28 images:\n",
+    "    image_grid = padded_instances.reshape((n_rows, images_per_row, size, size))\n",
+    "\n",
+    "    # Combine axes 0 and 2 (vertical image grid axis, and vertical image axis),\n",
+    "    # and axes 1 and 3 (horizontal axes). We first need to move the axes that we\n",
+    "    # want to combine next to each other, using transpose(), and only then we\n",
+    "    # can reshape:\n",
+    "    big_image = image_grid.transpose(0, 2, 1, 3).reshape(n_rows * size,\n",
+    "                                                         images_per_row * size)\n",
+    "    # Now that we have a big image, we just need to show it:\n",
+    "    plt.imshow(big_image, cmap = mpl.cm.binary, **options)\n",
     "    plt.axis(\"off\")"
    ]
   },
diff --git a/08_dimensionality_reduction.ipynb b/08_dimensionality_reduction.ipynb
index ecb8b9d..ab103af 100644
--- a/08_dimensionality_reduction.ipynb
+++ b/08_dimensionality_reduction.ipynb
@@ -947,19 +947,28 @@
    "metadata": {},
    "outputs": [],
    "source": [
+    "# EXTRA\n",
     "def plot_digits(instances, images_per_row=5, **options):\n",
     "    size = 28\n",
     "    images_per_row = min(len(instances), images_per_row)\n",
-    "    images = [instance.reshape(size,size) for instance in instances]\n",
+    "    # This is equivalent to n_rows = ceil(len(instances) / images_per_row):\n",
     "    n_rows = (len(instances) - 1) // images_per_row + 1\n",
-    "    row_images = []\n",
+    "\n",
+    "    # Append empty images to fill the end of the grid, if needed:\n",
     "    n_empty = n_rows * images_per_row - len(instances)\n",
-    "    images.append(np.zeros((size, size * n_empty)))\n",
-    "    for row in range(n_rows):\n",
-    "        rimages = images[row * images_per_row : (row + 1) * images_per_row]\n",
-    "        row_images.append(np.concatenate(rimages, axis=1))\n",
-    "    image = np.concatenate(row_images, axis=0)\n",
-    "    plt.imshow(image, cmap = mpl.cm.binary, **options)\n",
+    "    padded_instances = np.concatenate([instances, np.zeros((n_empty, size * size))], axis=0)\n",
+    "\n",
+    "    # Reshape the array so it's organized as a grid containing 28×28 images:\n",
+    "    image_grid = padded_instances.reshape((n_rows, images_per_row, size, size))\n",
+    "\n",
+    "    # Combine axes 0 and 2 (vertical image grid axis, and vertical image axis),\n",
+    "    # and axes 1 and 3 (horizontal axes). We first need to move the axes that we\n",
+    "    # want to combine next to each other, using transpose(), and only then we\n",
+    "    # can reshape:\n",
+    "    big_image = image_grid.transpose(0, 2, 1, 3).reshape(n_rows * size,\n",
+    "                                                         images_per_row * size)\n",
+    "    # Now that we have a big image, we just need to show it:\n",
+    "    plt.imshow(big_image, cmap = mpl.cm.binary, **options)\n",
     "    plt.axis(\"off\")"
    ]
   },