Next Gen UI demo (#1778)

First pass at a Next Generation UI demo app. The UI needs work, feedback
gratefully accepted.

## Pre-launch Checklist

- [x] I read the [Flutter Style Guide] _recently_, and have followed its
advice.
- [x] I signed the [CLA].
- [x] I read the [Contributors Guide].
- [x] I updated/added relevant documentation (doc comments with `///`).
- [x] All existing and new tests are passing.

If you need help, consider asking for advice on the #hackers-devrel
channel on [Discord].

<!-- Links -->
[Flutter Style Guide]:
https://github.com/flutter/flutter/wiki/Style-guide-for-Flutter-repo
[CLA]: https://cla.developers.google.com/
[Discord]: https://github.com/flutter/flutter/wiki/Chat
[Contributors Guide]:
https://github.com/flutter/samples/blob/main/CONTRIBUTING.md

next_gen_ui_demo/lib/common/reactive_widget.dart

@@ -0,0 +1,37 @@
+// Copyright 2023 The Flutter Authors. 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';
+
+import 'ticking_builder.dart';
+
+typedef ReactiveWidgetBuilder = Widget Function(
+    BuildContext context, double time, Size bounds);
+
+/// ReactiveWidget forces repainting a subtree on
+/// each frame for ambient animation.
+class ReactiveWidget extends StatefulWidget {
+  const ReactiveWidget({
+    super.key,
+    required this.builder,
+  });
+  final ReactiveWidgetBuilder builder;
+  @override
+  State<ReactiveWidget> createState() => _ReactiveWidgetState();
+}
+
+class _ReactiveWidgetState extends State<ReactiveWidget> {
+  @override
+  Widget build(BuildContext context) {
+    return TickingBuilder(
+      builder: (_, time) {
+        return LayoutBuilder(
+          builder: (context, constraints) {
+            return widget.builder(context, time, constraints.biggest);
+          },
+        );
+      },
+    );
+  }
+}