Very distinct strategies can be deployed to recognize and characterize an unknown environment or a shape. A recent and promising approach, especially in robotics, is to reduce the complexity of the exploratory units to a minimum. Here, we show that this frugal strategy can be taken to the extreme by exploiting the power of statistical geometry and introducing different invariant features. We show that an elementary robot devoid of any orientation or location system, exploring randomly, can access global information about an environment such as the values of the explored area and perimeter. The explored shapes are of arbitrary geometry and may even nonconnected. From a dictionary, this most simple robot can thus identify various shapes such as famous monuments and even read a text.