How to make a wavy circle?

Hello! I am trying to make a waved circle like the left one in the picture:
(I found this picture from http://www.kentchemistry.com/links/AtomicStructure/wavesElectrons.htm)

This is my attempt with LineRenderer:

 using System.Collections;
 using UnityEngine;
 
 [RequireComponent(typeof(LineRenderer))]
 public class Circle : MonoBehaviour {
     
     public int pointsNum = 120;
     public float radius = 2f;
 
     public float angleVel = 0.1f;
     public float speed = 0.5f;
     public float amplitude = 0.05f;
     public float rotateSpeed = 0.5f;
     public float rotateRatio = 30f;

     float startAngle = 0f;
     float angle = 0f;
     Vector3[] originalPos;
     
     LineRenderer line;
     int segments;
 
     void Start()
     {
         line = gameObject.GetComponent<LineRenderer>();
 
         segments = pointsNum - 1;
 
         line.numPositions = pointsNum;
         
         line.useWorldSpace = false;
 
         originalPos = new Vector3[pointsNum];
 
         CreatePoints();
     }
 
     void Update()
     {
             SimulateWave();
       
     }
 
     void CreatePoints()
     {
         float x;
         float y;
         float z = 0f;
 
         float ang = 0f;  // start from 0 degree
 
         for (int i = 0; i < pointsNum; i++)
         {
             x = Mathf.Sin(Mathf.Deg2Rad * ang) * radius;
             y = Mathf.Cos(Mathf.Deg2Rad * ang) * radius;
 
             line.SetPosition(i, new Vector3(x, y, z));
 
             originalPos[i] = line.GetPosition(i);
 
             ang += ((360f / segments) + (360f / segments) / pointsNum);
         }
     }
 
     void SimulateWave()
     {
 
         // Each frame a new wave
         startAngle += speed;
         angle = startAngle;
 
         // Loop through each point in the wave
         for (int i = 0; i < pointsNum; i++)
         {
             float x = Mathf.Cos(angle) * amplitude;
             float y = Mathf.Sin(angle) * amplitude;
             float z = 0;
             Vector3 wave = new Vector3(x, y, z);
 
             line.SetPosition(i, originalPos[i] + wave);
 
             angle += angleVel;
             //angle += (totalAngle/pointsNum);
         }
 
         // Rotate the circle
         Vector3 ro = new Vector3(0, 0, rotateRatio);
         Quaternion roQ = Quaternion.Euler(ro);
         transform.rotation = Quaternion.Slerp(transform.rotation, transform.rotation * roQ, rotateSpeed * Time.deltaTime);
         Debug.Log(AudioData.amplitudeBuffer * rotateRatio);
         
     }
 }

But the first point's and the last point's position don't match. It looks like:

(Just like the right one in first picture)

I think that's because my wave is not in a full cycle maybe?
Really hope someone could provide some guides to make a wavy circle.
Thank you!