opengl strange output from normalmap - c++

Question

I create a terrain grid with 1024x1024 points, generate a normal map from that and try to use it in my vertex/fragment shader. Im getting strange results when i draw normals from normalmap compared to normals passed from the vertex shader. I try to improve quality by increase the texture resolution up to 8192, but doesnt remove strange aliasing effect.
The same happens when i get the normal from neighbouring pixels in a heightmap.
How can i fix this?
normalmap texture creation:
uint16_t channels = 3;
GLuint Texture = m_frameBuffers;
float* pData = new float[width * height * channels];
glGenTextures(1, &Texture);
glBindTexture(GL_TEXTURE_2D, Texture);
for (uint16_t y = 0; y < height; ++y)
{
for (uint16_t x = 0; x < width; ++x)
{
uint32_t index = y * width + x;
pData[index * channels + 0] = (normals[index].x) * 0.5 + 0.5;
pData[index * channels + 1] = (normals[index].y) * 0.5 + 0.5;
pData[index * channels + 2] = (normals[index].z) * 0.5 + 0.5;
}
}
glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, width, height, 0, GL_RGB, GL_FLOAT, pData);
glGenerateMipmap(GL_TEXTURE_2D);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR_MIPMAP_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_REPEAT);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_REPEAT);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_R, GL_REPEAT);
delete[] pData;
++m_frameBuffers;
return Texture;
fragment shader:
vec3 normal = texture(normalMap, VertexIn.texcoord).rgb;
normal = normalize(normal * 2.0 - 1.0);
normal = normalize(vec3(normalmatrix*vec4(normal,1.0)));
edit: i uploaded better pictures to compare. it shows same area of a 1024x1024 grid, first is from vertex normals, second uses normal map with RGB16F