Wrong and weird lightning on a very simple mesh

Question

I've been trying to correctly generate 3D figures like planes, spheres and cubes. But I'm trying to apply illumination to them so I also generate normals.

Here's my output from a simple plane, I'm only using triangles and I'm using a positional light:

Vertice 0: 3.000000 3.000000 0.000000
Vertice 1: 3.000000 -3.000000 0.000000
Vertice 2: -3.000000 -3.000000 0.000000
Vertice 3: -3.000000 3.000000 0.000000
Normal: 0.000000 0.000000 1.000000
Normal: -0.000000 0.000000 1.000000

And here's the result:

Sometimes it lights it right and sometimes it shows in that way, with the 2 OBVIOUS triangles.

What do you think might be the reason for this?

---

Here's the vertex shader:

attribute highp vec4 vertices;
attribute highp vec3 normals;
uniform mediump mat4 projectMatrix;
uniform mediump mat4 viewMatrix;
uniform mediump mat4 modelMatrix;
out highp vec3 normal;
out highp vec4 pos_ws;
out lowp vec4 lightp_cs;

void main (void)
{
    vec4 PPos= vec4(3.0, 3.0, 3.0, 1.0);

gl_Position= projectMatrix*viewMatrix*modelMatrix*vertices;
normal= normals;
    pos_ws= viewMatrix*modelMatrix * vec4(vertices);
    lightp_cs= viewMatrix* PPos;
}

And this is the fragment shader:

in highp vec3 normal;
in highp vec4 pos_ws;
in lowp vec4 lightp_cs;

void main(void)
{
vec4 ambient= vec4 (0.276, 0.342, 0.417, 1.0);

vec4 DiffuseColor= vec4 (0.40234375, 0.40234375, 0.40234375, 1.0);

    vec4 PColor= vec4(0.7, 0.7, 0.7, 1.0);
    //vec4 PPos= vec4(3.0, 3.0, 3.0, 1.0);
vec3 PAtt= vec3(0.6, 0.050, 0.005);

// Para la luz puntual
    //vec4 vToLight= pos_ws - PPos;
    vec4 vToLight= pos_ws - lightp_cs;
vToLight= normalize(vToLight);
float distToLight= length(vToLight);
vec4 Vnormal= vec4(normal, 1.0);

    float cosNPL= clamp(dot(Vnormal, -vToLight), 0, 1);
float PLAtt= (PAtt.x + PAtt.y * distToLight + PAtt.z * distToLight * distToLight);

gl_FragColor= ambient + (DiffuseColor * (cosNPL * PColor)/PLAtt); // Luz Puntual
}

Answer 1

It's solved now.

datenwolf was right. I was only considering face's normals, since I started to calculate and give to opengl the vertices' normals, the plane is being rendered correctly.

I'll also take into account Spektre's answer, I guess you're talking about the normal matrix. I will do that too.

Since I'm just generating a plane, the real challenge will come when I start to generate a sphere. I also don't know if the order you pass the normals makes any difference (face normal, vertex normal, f, v, f, f, v, etc), I think it doesn't.

Anyway, thanks to everyone! :)