How to periodically set state?

As pskink and Günter mentioned, use a Timer. You can even use the periodic constructor that would fit well your scenario.

Note you don't need the asd() function. When you call setState(), the build method will be called automatically passing the new now property value.

If you want, use initState to set an initial value and, as in this example, setup the Timer.

import 'dart:async';
import 'package:flutter/material.dart';

void main() => runApp(MyApp());

class MyApp extends StatelessWidget {
  @override
  Widget build(BuildContext context) {
    return MaterialApp(title: 'Timer Periodic Demo', home: RopSayac());
  }
}

class RopSayac extends StatefulWidget {
  _RopSayacState createState() => _RopSayacState();
}

class _RopSayacState extends State<RopSayac> {
  String _now;
  Timer _everySecond;

  @override
  void initState() {
    super.initState();

    // sets first value
    _now = DateTime.now().second.toString();

    // defines a timer 
    _everySecond = Timer.periodic(Duration(seconds: 1), (Timer t) {
      setState(() {
        _now = DateTime.now().second.toString();
      });
    });
  }

  @override
  Widget build(BuildContext context) {
    return Container(
      child: Center(
        child: new Text(_now),
      ),
    );
  }
}

This recursive method should be enough for what you want. The seconds set as 1 will keep triggering setState each second, thus refreshing your widget tree.

void _timer() {
    Future.delayed(Duration(seconds: 1)).then((_) {
      setState(() {
        print("1 second closer to NYE!");
        // Anything else you want
      });
      _timer();
    });
  }