public class AnimatableHelperBase<T>
    {
        // Это attached property OriginalProperty. К нему мы будем привязывать свойство из VM,
        // и получать нотификацию об его изменении
        public static T GetOriginalProperty(DependencyObject obj) =>
            (T)obj.GetValue(OriginalPropertyProperty);
        public static void SetOriginalProperty(DependencyObject obj, T value) =>
            obj.SetValue(OriginalPropertyProperty, value);
        public static readonly DependencyProperty OriginalPropertyProperty =
            DependencyProperty.RegisterAttached(
                "OriginalProperty", typeof(T), typeof(AnimatableHelperBase<T>),
                new PropertyMetadata(OnOriginalUpdatedStatic));

        // это "производное" attached property, которое будет
        // анимированно "догонять" OriginalProperty
        public static T GetAnimatedProperty(DependencyObject obj) =>
            (T)obj.GetValue(AnimatedPropertyProperty);
        public static void SetAnimatedProperty(DependencyObject obj, T value) =>
            obj.SetValue(AnimatedPropertyProperty, value);
        public static readonly DependencyProperty AnimatedPropertyProperty =
            DependencyProperty.RegisterAttached(
                "AnimatedProperty", typeof(T), typeof(AnimatableHelperBase<T>));

        // это вызывается когда значение OriginalProperty меняется
        static void OnOriginalUpdatedStatic(DependencyObject o, DependencyPropertyChangedEventArgs e)
        {
            T newValue = (T)e.NewValue;
            // находим элемент, на котором меняется свойство
            FrameworkElement self = (FrameworkElement)o;
            AnimationTimeline animation = CreateAnimation(self, newValue);
            self.BeginAnimation(AnimatedPropertyProperty, animation);
        }

        protected static Func<FrameworkElement, T, AnimationTimeline> CreateAnimation;
    }

    public class AnimatableDoubleHelper : AnimatableHelperBase<double>
    {
        static AnimatableDoubleHelper()
        {
            CreateAnimation = (self, newValue) =>
                new DoubleAnimation(newValue, new Duration(TimeSpan.FromSeconds(0.3)));
        }
    }

    public class AnimatablePointHelper : AnimatableHelperBase<Point>
    {
        static AnimatablePointHelper()
        {
            CreateAnimation = (self, newValue) =>
                new PointAnimation(newValue, new Duration(TimeSpan.FromSeconds(0.3)));
        }
    }

--------------------

    class Tile : VM
    {
        (int x, int y) location;
        public (int x, int y) Location
        {
            get => location;
            set => Set(ref location, value);
        }

        string caption;
        public string Caption
        {
            get => caption;
            set => Set(ref caption, value);
        }
    }

--------------------

        public MainVM()
        {
            Tiles = new ObservableCollection<Tile>
            {
                new Tile { Caption="1", Location = (0, 0) },
                new Tile { Caption="2", Location = (1, 0) },
                new Tile { Caption="3", Location = (2, 0) },
                new Tile { Caption="4", Location = (2, 1) },
                new Tile { Caption="5", Location = (2, 2) },
                new Tile { Caption="6", Location = (1, 2) },
                new Tile { Caption="7", Location = (0, 2) },
                new Tile { Caption="8", Location = (0, 1) },
            };

            turnCommand = new RelayCommand(_ => TurnTiles());
        }

        void TurnTiles()
        {
            // Здесь используются фичи C# 7.0 и .NET Framework 4.7
            Dictionary<(int, int), (int, int)> transitions = new Dictionary<(int, int), (int, int)>
            {
                [(0, 0)] = (0, 1),
                [(1, 0)] = (0, 0),
                [(2, 0)] = (1, 0),
                [(2, 1)] = (2, 0),
                [(2, 2)] = (2, 1),
                [(1, 2)] = (2, 2),
                [(0, 2)] = (1, 2),
                [(0, 1)] = (0, 2),
            };
            foreach (var tile in Tiles)
                tile.Location = transitions[tile.Location];
        }

--------------------

    class XYToPointConverter : IValueConverter
    {
        public double TileWidth { get; set; }
        public double TileHeight { get; set; }

        public object Convert(object value, Type targetType, object parameter, CultureInfo culture)
        {
            var typedValue = ((int x, int y))value;
            return new Point(typedValue.x * TileWidth, typedValue.y * TileHeight);
        }

        public object ConvertBack(object value, Type targetType, object parameter, CultureInfo culture)
        {
            throw new NotImplementedException();
        }
    }

--------------------

                <Style>
                    <Setter Property="local:AnimatablePointHelper.OriginalProperty"
                            Value="{Binding Location, Converter={StaticResource XYToPointConverter}}"/>
                    <Setter Property="Canvas.Left"
                            Value="{Binding (local:AnimatablePointHelper.AnimatedProperty).X, RelativeSource={RelativeSource Self}}"/>
                    <Setter Property="Canvas.Top"
                            Value="{Binding (local:AnimatablePointHelper.AnimatedProperty).Y, RelativeSource={RelativeSource Self}}"/>
                </Style>