Application of the BBC micro:bit to real-time generation and wireless transmission of multi-wing chaotic attractors

The BBC micro:bit is a pocket-sized educational single-board computer that was designed to introduce school pupils to programming. In this work we show that the micro:bit V2 (Nordic nRF52833, 64~MHz ARM Cortex-M4F core) can be used for the real-time numerical generation of chaotic signals. Using MicroPython in the Mu~1.2.0 editor, we implement on the board (i) the logistic map, including sensitive dependence on initial conditions and a full bifurcation diagram; (ii) the Lorenz attractor; (iii) a recently proposed three-dimensional chaotic system with hyperbolic-tangent and absolute-value nonlinearities; and (iv) the family of multi-wing attractors obtained from that system through a generalized Julia-fractal transformation u+iv=K(x+iy)M+Z₀. All continuous-time systems are integrated on the board with a fixed-step fourth-order Runge--Kutta scheme in single precision, at 2--5.4~ms per step. The 0--1 test for chaos applied to a 28\,000-point time series computed on the board gives $K=0.9980$, in agreement with the value $K=0.9978$ obtained earlier from a high-precision computation. Multi-wing attractors with $2M=4,6,8,10$ and $12$ wings are reproduced directly on the board. The data are transferred to a computer over USB serial, over the board's 2.4~GHz radio to a second micro:bit (V1.5) acting as a receiver (no lost packets out of 10⁴), and over Bluetooth Low Energy to a web browser, where a purpose-built page acts as a virtual oscilloscope. The approach described in this work is particularly attractive both for teaching nonlinear dynamics to students and for rapid hardware prototyping of chaos-based applications.