Create a Texture2D from scratch, and modify it slightly each frame.

dynamicTexture.cs

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

public class dynamicTexture : MonoBehaviour
{
    public int width=32;
    public int height=32;

    void Start()
        {
        Texture2D texture = new Texture2D(width,height);
        var pixels = texture.GetPixels32(0);
        for (int j=0; j < height; j++)
            {
            for (int i=0; i < width; i++)
                {
                pixels[i+j*width] = new Color(j/(float)height,i/(float)width,0,0) + Random.ColorHSV()/10f;
                }
            }
        texture.SetPixels32(pixels);
        GetComponent<Renderer>().material.mainTexture = texture;
        texture.Apply();
        }

    void Update()
        {
        Texture2D texture = (Texture2D) GetComponent<Renderer>().material.mainTexture;
        texture.SetPixel(Random.Range(0,width), Random.Range(0,height), Color.black);
        texture.Apply();        
        }
}