While studying the mathematical process of graphing formulae, Canadian mathematician Jeff Tupper developed a formula that could be used to convert a number into an arbitrary bitmap image.
The formula, known as Tupper’s self-referential formula, is a mathematical inequality relationship that can actually be used to draw any image. However, when fed with a particular 543 digit number, called the “k” constant, the formula will actually plot itself.
The formula is mostly used for instructional purposes in a number of mathematics and computer science courses to demonstrate the concepts of self-reference and general graphing formulae, but can have other uses as well.
What the formula essentially does is convert the large input number into a sequence of points on a two dimensional graph. These dots on the graph come together to form a 17 pixel high by 106 pixel long bitmap picture recognisable by the human beings.
The value of “k” can be derived by drawing your chosen picture on the 17x106 matrix, reading off the binary number (dots are 1’s and blanks are 0’s), multiplying the result by 17 and then converting the output to an integer.
