Opengl ES 2.0, FBOs, and Fragment Shaders

Question

Here's my render loop:

1. Bind a custom FBO
2. Bind a texture (previously associated with the FBO as COLOR_ATTACHMENT0)
3. Render using a custom fragment shader which chooses fragment colors on the basis of a fractal algorithm. (If a fragment is not used by the algorithm, it is assigned the color black)
4. Rebind the window-provided framebuffer and renderbuffer. (on ios 5, this is the [view bindDrawable] method.
5. Clear the screen to white.
6. Render the fbo texture into a frame that is substantially smaller than the window itself.

Expected result: The fractal should appear in the smaller frame. The frame should have a black background. The rest of the screen should be white.

Current result: The entire screen is taken up by the fractal, as if I were rendering to the window provided fbo, and to my custom fbo/texture.

I don't really know what I'm doing wrong, so I'd be grateful for any help.

EDIT:

Fragment Shader:

void main()
{
   highp vec2 pix = gl_FragCoord.xy;
   lowp vec4 color = vec4(0.0,0.0,0.0,0.0);

   //determine if fragment is part of the fractal using the algorithm
   //if yes, change the value of the color vec4

   gl_FragColor = color;
}

FBO Initialization:

    //First create and bind the frame buffer
glGenFramebuffers(1, &frameBuffer);
glBindFramebuffer(GL_FRAMEBUFFER, frameBuffer);

//Create a texture
glGenTextures(1, &texture);
glBindTexture(GL_TEXTURE_2D, texture); 
glTexImage2D(GL_TEXTURE_2D, 0, GL_RGBA, width, height, 0, GL_RGBA, GL_UNSIGNED_BYTE, 0);
glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE); 
glTexParameterf(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE); 
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR); 
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR); 

//Attach the texture to the framebuffer
glFramebufferTexture2D(GL_FRAMEBUFFER, GL_COLOR_ATTACHMENT0, GL_TEXTURE_2D, texture, 0);

GLenum status = glCheckFramebufferStatus(GL_FRAMEBUFFER);    
if (status != GL_FRAMEBUFFER_COMPLETE)  {
    printf("\n Incomplete Frame Buffer!");
}

Render Loop:

{
glBindFramebuffer(GL_FRAMEBUFFER, frameBuffer);
glBindRenderbuffer(GL_RENDERBUFFER, texture);
glViewport(0, 0, width, height);

//Call the fractal render, basically a plane of 4 vertices happening through GL_TRIANGLE_STRIP, but that calls the fragment shader above.

[self.view bindDrawable];
glClearColor(1.0,1.0,1.0,1.0);

matrix4x4 mvp = multiplyMatrices(projectionMatrix, modelView);

glUseProgram(shaderId);
glBindBuffer(GL_ARRAY_BUFFER, vertexBuffer);
glVertexAttribPointer(positionLocation, 4, GL_FLOAT, GL_FALSE, 0, NULL);   
glBindBuffer(GL_ARRAY_BUFFER, texelBuffer);
glVertexAttribPointer(texelLocation, 2, GL_FLOAT, GL_FALSE, 0, NULL);

glUniformMatrix4fv(mvpLocation, 1, 0, mvp.val);
glActiveTexture(GL_TEXTURE0);
glBindTexture(GL_TEXTURE_2D, textureId);
glUniform1i(textureLocation, 0);

glDrawArrays(GL_TRIANGLE_STRIP, 0, tVertices);
}

I hope this helps. Please let me know if you'd like any more information on what I'm doing.

I also noticed something very strange happening.

If, after binding the FBO, I try

glClear(GL_COLOR_BUFFER_BIT);
glClearColor(1.0,0.0,0.0,0.5); 

...it is the window-provided framebuffer on which the clear actually happens.

Thank you guys for helping.