diff --git a/spacy/visualization.py b/spacy/visualization.py
index bde843a71..01d6b2b5e 100644
--- a/spacy/visualization.py
+++ b/spacy/visualization.py
@@ -18,34 +18,35 @@ class Visualizer:
             for token in doc
         ]
         children_lists = [[] for _ in range(len(doc))]
-        for child, head in enumerate(h for h in heads):
+        for child, head in enumerate(heads):
             if head != -1:
                 children_lists[head].append(child)
         all_indices_ordered_by_column = []
         indices_in_current_column = [i for i, h in enumerate(heads) if h == -1]
         while len(indices_in_current_column) > 0:
-            all_indices_ordered_by_column.extend(indices_in_current_column)
+            all_indices_ordered_by_column = (
+                indices_in_current_column + all_indices_ordered_by_column
+            )
             indices_in_current_column = [
                 i
                 for index_in_current_column in indices_in_current_column
                 for i in children_lists[index_in_current_column]
                 if i not in all_indices_ordered_by_column
             ]
-        all_indices_ordered_by_column = reversed(all_indices_ordered_by_column)
-        # -1: no arrow; None: not yet set
-        horizontal_arrow_positions = [
+        # -1: root token with no arrow; 0: length not yet set
+        horizontal_line_lengths = [
             -1
             if heads[i] == -1
-            else 0
+            else 1
             if len(children_lists[i]) == 0 and abs(heads[i] - i) == 1
-            else None
+            else 0
             for i in range(len(doc))
         ]
-        while None in horizontal_arrow_positions:
+        while 0 in horizontal_line_lengths:
             for working_token_index in (
                 i
                 for i in all_indices_ordered_by_column
-                if horizontal_arrow_positions[i] is None
+                if horizontal_line_lengths[i] == 0
             ):
                 first_index_in_relation = min(
                     working_token_index,
@@ -55,61 +56,43 @@ class Visualizer:
                     working_token_index,
                     heads[working_token_index],
                 )
-                inbetween_indexes = range(
-                    first_index_in_relation + 1, second_index_in_relation
-                )
-                inbetween_horizontal_arrow_positions = horizontal_arrow_positions[
-                    first_index_in_relation + 1 : second_index_in_relation
-                ]
-                if (
-                    -1 in inbetween_horizontal_arrow_positions
-                    and None in inbetween_horizontal_arrow_positions
-                ):
-                    continue
-                if None in (
-                    horizontal_arrow_positions[i]
-                    for i in children_lists[working_token_index]
-                ):
-                    continue
                 if len(children_lists[working_token_index]) > 0:
-                    working_horizontal_arrow_position = (
-                        max(
-                            [
-                                horizontal_arrow_positions[i]
-                                for i in children_lists[working_token_index]
-                            ]
-                        )
-                        + 1
+                    working_horizontal_arrow_position = max(
+                        [
+                            horizontal_line_lengths[i]
+                            for i in children_lists[working_token_index]
+                        ]
                     )
                 else:
-                    working_horizontal_arrow_position = -1
+                    working_horizontal_arrow_position = 0
                 for inbetween_index in (
                     i
-                    for i in inbetween_indexes
+                    for i in range(
+                        first_index_in_relation + 1, second_index_in_relation
+                    )
                     if i not in children_lists[working_token_index]
-                    and horizontal_arrow_positions[i] is not None
+                    and horizontal_line_lengths[i] != 0
                 ):
                     working_horizontal_arrow_position = max(
                         working_horizontal_arrow_position,
-                        horizontal_arrow_positions[inbetween_index]
+                        horizontal_line_lengths[inbetween_index] - 1
                         if inbetween_index in children_lists[heads[working_token_index]]
-                        else horizontal_arrow_positions[inbetween_index] + 1,
+                        else horizontal_line_lengths[inbetween_index],
                     )
                     for child_horizontal_arrow_position in (
-                        horizontal_arrow_positions[i]
+                        horizontal_line_lengths[i]
                         for i in children_lists[working_token_index]
                         if (i < first_index_in_relation or i > second_index_in_relation)
-                        and horizontal_arrow_positions[i] is not None
+                        and horizontal_line_lengths[i] != 0
                     ):
                         working_horizontal_arrow_position = max(
                             working_horizontal_arrow_position,
-                            child_horizontal_arrow_position + 1,
+                            child_horizontal_arrow_position,
                         )
-                if working_horizontal_arrow_position > -1:
-                    horizontal_arrow_positions[
-                        working_token_index
-                    ] = working_horizontal_arrow_position
-        print(horizontal_arrow_positions)
+                horizontal_line_lengths[working_token_index] = (
+                    working_horizontal_arrow_position + 1
+                )
+        print(horizontal_line_lengths)
 
 
 import spacy