Tidyup animations sample (#1672)

* Tidyup

* Drop `flutterAnimateDemos`

animations/lib/src/basics/animated_builder.dart

@@ -0,0 +1,78 @@
+// Copyright 2019 The Flutter team. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+import 'package:flutter/material.dart';
+
+class AnimatedBuilderDemo extends StatefulWidget {
+  const AnimatedBuilderDemo({super.key});
+  static const String routeName = 'basics/animated_builder';
+
+  @override
+  State<AnimatedBuilderDemo> createState() => _AnimatedBuilderDemoState();
+}
+
+class _AnimatedBuilderDemoState extends State<AnimatedBuilderDemo>
+    with SingleTickerProviderStateMixin {
+  static const Color beginColor = Colors.deepPurple;
+  static const Color endColor = Colors.deepOrange;
+  Duration duration = const Duration(milliseconds: 800);
+  late AnimationController controller;
+  late Animation<Color?> animation;
+
+  @override
+  void initState() {
+    super.initState();
+
+    controller = AnimationController(vsync: this, duration: duration);
+    animation =
+        ColorTween(begin: beginColor, end: endColor).animate(controller);
+  }
+
+  @override
+  void dispose() {
+    controller.dispose();
+    super.dispose();
+  }
+
+  @override
+  Widget build(BuildContext context) {
+    return Scaffold(
+      appBar: AppBar(
+        title: const Text('AnimatedBuilder'),
+      ),
+      body: Center(
+        // AnimatedBuilder handles listening to a given animation and calling the builder
+        // whenever the value of the animation change. This can be useful when a Widget
+        // tree contains some animated and non-animated elements, as only the subtree
+        // created by the builder needs to be re-built when the animation changes.
+        child: AnimatedBuilder(
+          animation: animation,
+          builder: (context, child) {
+            return MaterialButton(
+              color: animation.value,
+              height: 50,
+              minWidth: 100,
+              child: child,
+              onPressed: () {
+                if (controller.status == AnimationStatus.completed) {
+                  controller.reverse();
+                } else {
+                  controller.forward();
+                }
+              },
+            );
+          },
+          // AnimatedBuilder can also accept a pre-built child Widget which is useful
+          // if there is a non-animated Widget contained within the animated widget.
+          // This can improve performance since this widget doesn't need to be rebuilt
+          // when the animation changes.
+          child: const Text(
+            'Change Color',
+            style: TextStyle(color: Colors.white),
+          ),
+        ),
+      ),
+    );
+  }
+}