Statement

Ever since Marcus (a famous Dutch abstractionist) heard of fractals, he made them the main topic of his canvases. Every morning, the artist takes a piece of graph paper and starts making a model of his future canvas, by selecting a rectangular area of N × N squares and painting some of these squares black. Then, he takes a clean square piece of paper and paints the fractal using the following algorithm: (1) [1.] The paper is divided into N^2 identical squares and some of them are painted black according to the model. (2) [2.] Every square that remains white is divided into N^2 smaller squares and some of them are painted black according to the model. (3) [… ] (4) [K.] Repeat step 2. At the end of the process, a canvas consisting of N^K × N^K black and white squares is produced. Unfortunately, this tiresome work demands too much time from his painting genius. Marcus has been dreaming of making the process automatic to move to making 3D or even 4D fractals: help him!