With the rapid progress in computer science, including artificial intelligence, big data and cloud computing, full-space spot generation can be pivotal to many practical applications, such as facial recognition, motion detection, augmented reality, etc. These opportunities may be achieved by using diffractive optical elements (DOEs) or light detection and ranging (LIDAR). However, DOEs suffer from intrinsic limitations, such as demanding depth-controlled fabrication techniques, large thicknesses (more than the wavelength), Lambertian operation only in half space, etc. LIDAR nevertheless relies on complex and bulky scanning systems, which hinders the miniaturization of the spot generator. Here, inspired by a Lambertian scatterer, we report a Hermitian-conjugate metasurface scrambling the incident light to a cloud of random points in full space with compressed information density, functioning in both transmission and reflection spaces. Over 4044 random spots are experimentally observed in the entire space, covering angles at nearly 90°. Our scrambling metasurface is made of amorphous silicon with a uniform subwavelength height, a nearly continuous phase coverage, a lightweight, flexible design, and low-heat dissipation. Thus, it may be mass produced by and integrated into existing semiconductor foundry designs. Our work opens important directions for emerging 3D recognition sensors, such as motion sensing, facial recognition, and other applications.