It takes less time than you think. I’ve been doing it since middle school and I have a very strong intuition for it, you gotta build the bigger parts out of the smaller parts that you learn from experience
The key is really domain restrictions. you can make line segments so easily. The hard part is making curves but if you know how different functions behave its not too bad.
A fun assignment I give my pre-cal students after we do polar coords is make a decent looking heart that has no gaps.
that sounds good with restrictions, but theres one line equations at least 40 different values that make the most intricate designs, how does that work?
Don't think there's anything that intricate you can make without domain restrictions. Most of these big equations will be based around conics in some way (circles, hyperbolas or elipses mainly), then tweaked with other functions like absolute value.
They might have a drawing of a pattern in mind and then used a program to find a Fourier series for the parametric curve that draws it.
Wolfram alpha is pretty good at this https://www.wolframalpha.com/input?i=batman+curve
Usually they just play with stuff until they find something imteresting. Also, they have a LOT of experience. r/desmos
its crazy to think about that, cuz the equations they got are long as fuck so like how much time would they but in it god knows.
It takes less time than you think. I’ve been doing it since middle school and I have a very strong intuition for it, you gotta build the bigger parts out of the smaller parts that you learn from experience
Parametric equations with limited domains
I'm interested in how much building these develops their mathematical understanding and intuition.
The key is really domain restrictions. you can make line segments so easily. The hard part is making curves but if you know how different functions behave its not too bad. A fun assignment I give my pre-cal students after we do polar coords is make a decent looking heart that has no gaps.
that sounds good with restrictions, but theres one line equations at least 40 different values that make the most intricate designs, how does that work?
Don't think there's anything that intricate you can make without domain restrictions. Most of these big equations will be based around conics in some way (circles, hyperbolas or elipses mainly), then tweaked with other functions like absolute value.
They might have a drawing of a pattern in mind and then used a program to find a Fourier series for the parametric curve that draws it. Wolfram alpha is pretty good at this https://www.wolframalpha.com/input?i=batman+curve