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/ticking_builder.dart

@@ -0,0 +1,40 @@
+// 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 'package:flutter/scheduler.dart';
+
+/// TickingBuilder is for ambient animation to be run
+/// on each frame.
+class TickingBuilder extends StatefulWidget {
+  const TickingBuilder({super.key, required this.builder});
+  final Widget Function(BuildContext context, double time) builder;
+  @override
+  State<TickingBuilder> createState() => _TickingBuilderState();
+}
+
+class _TickingBuilderState extends State<TickingBuilder>
+    with SingleTickerProviderStateMixin {
+  late final Ticker _ticker;
+  double _time = 0.0;
+
+  @override
+  void initState() {
+    super.initState();
+    _ticker = createTicker(_handleTick)..start();
+  }
+
+  @override
+  void dispose() {
+    _ticker.dispose();
+    super.dispose();
+  }
+
+  void _handleTick(Duration elapsed) {
+    setState(() => _time = elapsed.inMilliseconds.toDouble() / 1000.0);
+  }
+
+  @override
+  Widget build(BuildContext context) => widget.builder.call(context, _time);
+}