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Rubik-Scrambler
This is something I am working on to help me learn about HTML, JavaScript, and CSS! It only supports the 3x3 but you can use it for a 2x2 (I am going to add more cubes but just don't have the motivation to do it). Hope you learn about this too! Only used in chrome but could be supported for other browsers.
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SurveyJS
Open-Source JSON Form Builder to Create Dynamic Forms Right in Your App. With SurveyJS form UI libraries, you can build and style forms in a fully-integrated drag & drop form builder, render them in your JS app, and store form submission data in any backend, inc. PHP, ASP.NET Core, and Node.js.
I have created a random scrambler that creates a list of notations for people to solve, although not fancy it still is well developed for a beginner webpage designer and programmer! It is available on GitHub with source code shown for anyone to edit, share, use, etc. to their heart's content! https://github.com/TheRedBasic/Rubik-Scrambler