Butterfly Network is a 72 × 96 in. acrylic on canvas painting by RIT Imaging Science alum Juliet Fiss. The painting celebrates the fast Fourier transform (FFT), an essential algorithm in Imaging Science. The FFT computes the frequency spectrum of a digital signal.

The top section of the painting represents the original domain of the signal. If the signal represents a line of pixels in an image, then the original domain is the spatial domain. This section shows the waveform of the signal as composed of sinusoids of different frequencies.

The middle sections of the painting illustrate the mathematics that compute a 32-point FFT. Below the original domain is the bit-reverse index step. Square mosaic tiles represent the indices from 0 to 31 in binary and reverse-binary. Lines drawn between corresponding bit-reverse index pairs create the blue and green diamond-like structure.

The middle of the painting is the butterfly network. The name Butterfly Network comes from the description of the mathematical structure of the FFT in scientific literature. One “X” shape is traditionally called a butterfly, and the arrangement of butterflies to form the data flow network of the FFT is called a butterfly network. The FFT is a recursive divide-and-conquer algorithm that calls two half-size FFTs at each stage. Because the painting represents a 32-point FFT, there are five rows of butterflies. The rows of blue circles represent the roots of unity, which are used in the FFT computation.

The bottom section of the painting represents the frequency spectrum of the signal, visualized as a rainbow of vibrant colors.