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In this paper, we define fractal bases and fractal frames of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="script">L</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>I</mi><mo>×</mo><mi>J</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <i>I</i> and <i>J</i> are real compact intervals, in order to approximate two-dimensional square-integrable maps whose domain is a rectangle, using the identification of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="script">L</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>I</mi><mo>×</mo><mi>J</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> with the tensor product space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="script">L</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>I</mi><mo>)</mo></mrow><mo>⨂</mo><msup><mi mathvariant="script">L</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>J</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>. First, we recall the procedure of constructing a fractal perturbation of a continuous or integrable function. Then, we define fractal frames and bases of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi mathvariant="script">L</mi><mn>2</mn></msup><mrow><mo>(</mo><mi>I</mi><mo>×</mo><mi>J</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> composed of product of such fractal functions. We also obtain weaker families as Bessel, Riesz and Schauder sequences for the same space. Additionally, we study some properties of the tensor product of the fractal operators associated with the maps corresponding to each variable.