Parametric curve between two points

I have a start point and an end point, I’m looking to create a parametric curve line between those two points. So the shape of the curve can be manipulated via the sliders.

I did manage to create something along these lines however it was utter chaotic and messy, surely there is a simple or straight forward way to go about this.

Would anyone know where to look?

image for reference.

After something similar to this end result

You could implement something like a self-avoiding random, two-dimensional walk with strict angular rules.

I’ve since moved onto this solution and is far cleaner than my original, is this on that same track?

the curve components at the beginning just contain line(s)

I don’t know, but does it work for you?

In some ways.

I was able to create 3 curves which can be controlled parametrically and then plugged into a grid.

However I now understood what you meant, and that may lead to a better result i’ll probably have issues with self intersecting lines and other problems faced with ‘random walk’

Sounds alright!

What is your goal exactly? Do you want to have a catalogue of generated curves that are then mapped to a grid?

Essentially I want to be able to create a set of curves parametrically, these curves are then mapped onto a grid, that grid is split into boundaries and each section coloured black and white, and or greyscale.
The grid is plugged into the component Biomorpher and the parametric number sliders that were controlling the curves are also plugged into Biomorpher.
Biomorpher then generates and evolves a set of curves which change the design over time.

Essentially its a deformation map, generatively designed.

I’m just trying to figure out the best way to essentially draw up those initial curves.