Generating a normal map from a height map?

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Example GLSL code from my water surface rendering shader:

#version 130
uniform sampler2D unit_wave
noperspective in vec2 tex_coord;
const vec2 size = vec2(2.0,0.0);
const ivec3 off = ivec3(-1,0,1);

    vec4 wave = texture(unit_wave, tex_coord);
    float s11 = wave.x;
    float s01 = textureOffset(unit_wave, tex_coord, off.xy).x;
    float s21 = textureOffset(unit_wave, tex_coord, off.zy).x;
    float s10 = textureOffset(unit_wave, tex_coord, off.yx).x;
    float s12 = textureOffset(unit_wave, tex_coord, off.yz).x;
    vec3 va = normalize(vec3(size.xy,s21-s01));
    vec3 vb = normalize(vec3(size.yx,s12-s10));
    vec4 bump = vec4( cross(va,vb), s11 );

The result is a bump vector: xyz=normal, a=height

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