The ability to make custom patterns is quite helpful but learning how to make patterns that repeat seamlessly in Illustrator makes it even better. Patterns that will show where the edges repeat may ...

It’s been just months since researchers reported the first “einstein” — a single tile that can cover an infinite plane, but only with a pattern that never repeats (SN: 3/24/23). Now, the same team has ...

Remember the graph paper you used at school, the kind that's covered with tiny squares? It's the perfect illustration of what mathematicians call a "periodic tiling of space", with shapes covering an ...

The original version of this story appeared in Quanta Magazine. If you want to tile a bathroom floor, square tiles are the simplest option—they fit together without any gaps in a grid pattern that can ...

Most people do not repeat mistakes because they enjoy pain. They repeat them because familiarity feels safer than change. We tell ourselves we will do things differently next time, yet find ourselves ...

Many people repeat the same mistakes, face similar conflicts, and carry old emotional wounds. The Bhagavad Gita explains that these patterns persist because unhealed emotions remain in the mind and ...