It took me a while to figure out how to use this. The idea is to visualize complex number mappings. You draw on the left square and the result is drawn on the right square. The result is generated by either a Φ function (mapping the complex value coordinates to new coordinates) or an f function (mapping the complex value to another complex value), but not both. You can animate either function by using t as a parameter. t has the specified constant value when not animating. You can't iterate, so this won't make fractals.
This could profit a lot from an example button
Yes, but you can also play around with it. x,y maps to u,v where t is a constant that may be animated and you can use many functions. Nice to build intuition. Here is an example:
This is very cool. I do think you could boost engagement a lot by offering a dropdown menu of transforms that you know work well and result in cool visual transformations. It would also be cool to have a palette of recognizable shapes (like letters, numbers, emoji) that you could quickly enter in and see how they get transformed instead of just freehand drawing and lines.
I like how on a touch screen using different parameters somehow affects your feeling of drawing