So today my Windows 10 was updating for about 40 minutes (probably patch for Meltdown vulnerability) and this has taken a heavy toll. Put this Component on a GameObject which has a banch of children SpriteRenderers. Play with parameters. Have fun.

demo.gif

Spinner.cs

using UnityEngine;

namespace Tests.Spinner
{
    public class Spinner : MonoBehaviour
    {
        private class Part
        {
            private Data _data;
            private Transform _transform;
            private SpriteRenderer _sprite;
            private float _phase;

            public Part(Data data, float phase, SpriteRenderer sprite)
            {
                _data = data;
                _phase = phase;
                _sprite = sprite;
                _transform = sprite.transform;
            }

            public void Update(float dt)
            {
                _phase = Mathf.Repeat(_phase + dt * _data.speed, 2.0f);

                float t = 1.0f - _phase;
                float p = Mathf.Pow(Mathf.Abs(t), _data.pow) * Mathf.Sign(t);
                float theta = 2.0f * Mathf.PI * (p + _data.offset);

                Vector3 position = default(Vector3);
                position.x = _data.radius * Mathf.Cos(theta);
                position.y = _data.radius * Mathf.Sin(theta);
                _transform.localPosition = position;

                var color = _sprite.color;
                color.a = Mathf.Sign((_phase - _data.clip) * (2.0f - _data.clip - _phase));
                _sprite.color = color;
            }
        }

        private struct Data
        {
            public float offset;
            public float radius;
            public float speed;
            public float clip;
            public float pow;
        }

        [SerializeField]
        private float _radius = 0.25f;
        [SerializeField]
        private float _speed = 0.7f;
        [SerializeField]
        private float _pow = 0.7f;
        [SerializeField]
        private float _offset = -0.25f;
        [SerializeField]
        private float _lag = 0.08f;
        [SerializeField]
        private float _clip = 0.2f;

        private Part[] _parts;
        private Data _data;

        private void Awake()
        {
            StoreData();
            CaptureParts();
        }

        private void OnValidate()
        {
            StoreData();
            CaptureParts();
        }

        private void Update()
        {
            float dt = Time.deltaTime;
            foreach (var part in _parts)
                part.Update(dt);
        }

        private void StoreData()
        {
            _data = new Data()
            {
                offset = _offset,
                radius = _radius,
                speed = _speed,
                clip = _clip,
                pow = _pow
            };
        }

        private void CaptureParts()
        {
            var sprites = GetComponentsInChildren<SpriteRenderer>();
            int count = sprites.Length;
            _parts = new Part[count];
            for (int i = 0; i < count; ++i)
            {
                var sprite = sprites[i];
                var part = new Part(_data, i * _lag, sprite);
                _parts[i] = part;
            }
        }
    }
}