We love creature sprites like this image of Ivysaur:

Sprites show surprising levels of detail despite their small image sizes. However, under every beautiful sprite is a matrix of numbers. Sprite of this size, whether used in games, websites, or other forms of media, can be expressed with 96 x 96 x 4 x 255 values.

Since every sprite has a unique mathematical fingerprint, we wondered if we could discover new creatures in the vector space of such images. We were excited to get creative in the face of a daunting mathematical challenge.

We applied a one-way transformation to all of the sprites, reducing them to 96 x 96 = 9216 component vectors. With five color values for each component, this still left a search space of over five hundred quadrillion (17 zeros) possible vectors. Far too many for humans to look at individually.

We applied a slew of data mining, machine learning, artificial intelligence, and deep learning techniques in pursuit of new, never-before-seen creature sprites. Methods implemented include:

• Principle Components Analysis
• K-Means Clustering
• Logistic Regression
• Kernel Smoothing
• Genetic Algorithms
• Linear Optimization
• Generative Adversarial Neural Networks
• Recommender Systems

In our search, we uncovered many, many, many pixelated red herrings as well as a handful of new creature-like sprites. They are "rough around the edges" but born entirely out of mathematics and computer science.

We developed Jupyter notebooks and a website to share our findings. The results show intriguing clusters of creatures and curious mutations of prospective sprites.

View methods and results on our website.

We also applied our sprite/vector transformation process to create a tool that allows users to search for sprites by drawing them. We have turned off the server that supports this, so the draw to search feature on the website will not work.