Abstract: Here, we introduce a new class of computer which does not use any circuit or logic gate. In fact, no program needs to be written: it learns by itself and writes its own program to solve a problem. Gödel’s incompleteness argument is explored here to devise an engine where an astronomically large number of “if-then” arguments are allowed to grow by self-assembly, based on the basic set of arguments written in the system, thus, we explore the beyond Turing path of computing but following a fundamentally different route adopted in the last half-a-century old non-Turing adventures. Our hardware is a multilayered seed structure. If we open the largest seed, which is the final hardware, we find several computing seed structures inside, if we take any of them and open, there are several computing seeds inside. We design and synthesize the smallest seed, the entire multilayered architecture grows by itself. The electromagnetic resonance band of each seed looks similar, but the seeds of any layer shares a common region in its resonance band with inner and upper layer, hence a chain of resonance bands is formed (frequency fractal) connecting the smallest to the largest seed (hence the name invincible rhythm or Ajeya Chhandam in Sanskrit). The computer solves intractable pattern search (Clique) problem without searching since the right pattern written in it spontaneously replies back to the questioner. To learn, the hardware filters any kind of sensory input image into several layers of images, each containing basic geometric polygons (fractal decomposition), and builds a network among all layers, multi-sensory images are connected in all possible ways to generate “if” and “then” argument. Several such arguments and decisions (phase transition from “if” to “then”) self-assemble and form the two giant columns of arguments and rules of phase transition. Any input question is converted into a pattern as noted above, and these two astronomically large columns project a solution. The driving principle of computing is synchronization and de-synchronization of network paths, the system drives towards highest density of coupled arguments for maximum matching. Memory is located at all layers of the hardware. Learning, computing occurs everywhere simultaneously. Since resonance chain connects all computing seeds, wireless processing is feasible without a screening effect. The computing power is increased by maximizing the density of resonance states and bandwidth of the resonance chain together. We discovered this remarkable computing while studying the human brain, so we present a new model of the human brain in terms of an experimentally determined resonance chain with bandwidth 10−15 Hz (complete brain with all sensors) to 10+15 Hz (DNA) along with its implementation using a pure organic synthesis of entire computer (brain jelly) in our lab, software prototype as proof of concept and finally a new fourth circuit element (Hinductor) based beyond Complementary metal-oxide semiconductor (CMOS) hardware is also presented.