diff --git a/CHANGELOG.md b/CHANGELOG.md
index e14bd69a6..63116cf01 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,11 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## Unreleased
+
+### Fixed
+
+- Fixed infinite loop when appending Text to same instance https://github.com/Textualize/rich/pull/3480
 
 ## [13.8.0] - 2024-08-26
 
diff --git a/rich/text.py b/rich/text.py
index 69e19b645..1f5353364 100644
--- a/rich/text.py
+++ b/rich/text.py
@@ -998,7 +998,7 @@ def append(
                 self._text.append(text.plain)
                 self._spans.extend(
                     _Span(start + text_length, end + text_length, style)
-                    for start, end, style in text._spans
+                    for start, end, style in text._spans.copy()
                 )
                 self._length += len(text)
         return self
@@ -1020,7 +1020,7 @@ def append_text(self, text: "Text") -> "Text":
         self._text.append(text.plain)
         self._spans.extend(
             _Span(start + text_length, end + text_length, style)
-            for start, end, style in text._spans
+            for start, end, style in text._spans.copy()
         )
         self._length += len(text)
         return self
diff --git a/tests/test_text.py b/tests/test_text.py
index 704462b45..1a22e79d2 100644
--- a/tests/test_text.py
+++ b/tests/test_text.py
@@ -1001,3 +1001,14 @@ def test_append_tokens() -> None:
     output = capture.get()
     print(repr(output))
     assert output == "long text that will be wrapped with a \ncontrol code \n\n"
+
+
+def test_append_loop_regression() -> None:
+    """Regression text for https://github.com/Textualize/rich/issues/3479"""
+    a = Text("one", "blue")
+    a.append(a)
+    assert a.plain == "oneone"
+
+    b = Text("two", "blue")
+    b.append_text(b)
+    assert b.plain == "twotwo"