ChaosTrail.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

[RequireComponent(typeof(LineRenderer))]
public class ChaosTrail : MonoBehaviour {

    public float minVertexDistance = 0.1f;
    public float maxPoints = 500;

    private LineRenderer lineRenderer; 

    // use an array as a ring buffer to avoid shuffling as points are added. 
    private List<Vector3> points;

    // Use this for initialization
    void Awake () {
        Init();
    }

    public void Init () {
        lineRenderer = GetComponent<LineRenderer>();
        points = new List<Vector3>();
    }

    public void AddPoint(Vector3 point) {
        if (points.Count >= maxPoints) {
            points.RemoveAt(0);
        }
        points.Add(point);
        // copy the points into the LineRenderer
        lineRenderer.positionCount = points.Count;
        int i = 0; 
        foreach (Vector3 p in points) {
            lineRenderer.SetPosition(i++, p);
        }
    }

}