Which browser by Mikuláš Patočka can operate in text and graphical modes? Links. It is a free-software web browser that combines a text interface with graphical rendering, making it unusual among lightweight browsers.
Patočka developed the original Links in the Czech Republic, and the project began in 1999. Its text mode was designed to preserve useful graphical-user-interface features, including menus and pop-up windows, within a text-only environment. It can render tables and frames and supports both color and monochrome terminals.
The graphical version became especially distinctive because it could work without the X Window System. On Unix-like systems, Links could draw through SVGAlib or directly through the graphics-card framebuffer. It also supports different font sizes and spatial antialiasing, although modern web compatibility is limited and JavaScript support was later removed.
A common mix-up is ELinks, which is a fork based on Links 0.9, not the original browser named in the question. Lynx and w3m are also text-oriented browsers, but Links is the one specifically associated with both text and graphical modes.