How do I texture a mesh programatically

I am trying to generate a mesh that will be a rock and I would like to texture it. I looked around, but could not figure how to do this. I use this code to generate a mesh, it's kinda ugly, but works for now:

     void CreateRock() 
     {
         GameObject rockObject = new GameObject();
         rockObject.transform.position = new Vector3 ( 0, 2, 0 );
         
         MeshFilter mf = rockObject.AddComponent < MeshFilter >();
         MeshRenderer mr = rockObject.AddComponent < MeshRenderer > ();
         
         Vector3[] verts = new Vector3[ 12 ];
         int[] tri = new int[10 * 3 * 2];
         
         // bottom
         float size = 0.75f;
         float height = 0;
         verts[0] = new Vector3(  size, height, -size );
         verts[1] = new Vector3(  size, height,  size );
         verts[2] = new Vector3( -size, height,  size );
         verts[3] = new Vector3( -size, height, -size );
 
         // center
         size = 1.25f;
         height = 3;
         verts[4] = new Vector3(  size, height, -size );
         verts[5] = new Vector3(  size, height,  size );
         verts[6] = new Vector3( -size, height,  size );
         verts[7] = new Vector3( -size, height, -size );
 
         // top
         size = 0.5f;
         height = 4;
         verts[ 8] = new Vector3(  size, height, -size );
         verts[ 9] = new Vector3(  size, height,  size );
         verts[10] = new Vector3( -size, height,  size );
         verts[11] = new Vector3( -size, height, -size );
 
 
 
         //triangles (clockwise)
         // bottom
         // 0, 1, 2
         // 0, 2, 3
 
         tri[0] = 0;
         tri[1] = 1;
         tri[2] = 2;
         
         tri[3] = 0;
         tri[4] = 2;
         tri[5] = 3;
 
         // bottom right
         // 0, 5, 1
         // 0, 4, 5
 
         tri[6] = 0;
         tri[7] = 5;
         tri[8] = 1;
         
         tri[9] = 0;
         tri[10] = 4;
         tri[11] = 5;
 
         // bottom front
         // 0, 7, 4
         // 0, 3, 7
 
         tri[12] = 0;
         tri[13] = 7;
         tri[14] = 4;
 
         tri[15] = 0;
         tri[16] = 3;
         tri[17] = 7;
 
         // bottom left
         // 3, 2, 6
         // 3, 6, 7
 
         tri[18] = 3;
         tri[19] = 2;
         tri[20] = 6;
 
         tri[21] = 3;
         tri[22] = 6;
         tri[23] = 7;
 
         // bottom back
         // 2, 1, 5
         // 2, 5, 6
 
         tri[24] = 2;
         tri[25] = 1;
         tri[26] = 5;
 
         tri[27] = 2;
         tri[28] = 5;
         tri[29] = 6;
 
         // top right
         // 4, 8, 9
         // 4, 9, 5
 
         tri[30] = 4;
         tri[31] = 8;
         tri[32] = 9;
 
         tri[33] = 4;
         tri[34] = 9;
         tri[35] = 5;
 
         // top front
         // 7, 11, 8
         // 7, 8, 4
 
         tri[36] = 7;
         tri[37] = 11;
         tri[38] = 8;
 
         tri[39] = 7;
         tri[40] = 8;
         tri[41] = 4;
 
         // top left
         // 11, 6, 10
         // 11, 7, 6
 
         tri[42] = 11;
         tri[43] = 6;
         tri[44] = 10;
 
         tri[45] = 11;
         tri[46] = 7;
         tri[47] = 6;
 
         // top back
         // 6, 5, 9
         // 6, 9, 10
 
         tri[48] = 6;
         tri[49] = 5;
         tri[50] = 9;
 
         tri[51] = 6;
         tri[52] = 9;
         tri[53] = 10;
 
         // top
         // 10, 9, 8
         // 11, 10, 8
 
         tri[54] = 10;
         tri[55] = 9;
         tri[56] = 8;
 
         tri[57] = 11;
         tri[58] = 10;
         tri[59] = 8;
 
         
         Mesh mesh = new Mesh();
         mesh.name = "Rock";
         mesh.vertices = verts;
         mesh.triangles = tri;
         mesh.RecalculateNormals();
         mf.mesh = mesh;
         
         mr.material = this.defaultRockMaterial;
     }

This works, and I see this:

I would like to apply this kind of texture to it. I would like the top to be generally green and bottom to be black. Maybe have some sort of wave effect where the color changes. So, here is a sample texture:

I guess I should be calculating UVs for the mesh, but not sure where to start. Halp please!