Scientific Algorithms that can produce imagery, pseudocode perhaps?

I have a client who is based in the field of mathematics. We are developing, amongst other things, a website. I like to create a mock-up of a drawing tool that can produce some imagery in the background based on some scientific algorithms. The intention being that the client, later, may create their own. (They use emacs for everything, great client.)

I'm looking for an answer about where or what to search. Not code specific, pseudocode even, as we can adapt and have not yet settled on a platform.

I'm afraid my mathematics stops at the power of two and some trigonometry. Appreciated if they're are any mathematics related students/academics how could enlighten me? What to search for will be accepted?

Edit: To summarise/clarify, I want to draw pretty pictures (the design perspective). I want them to have some context (i.e. not just for the sake of pretty images but have some explanation available). In essence I would to create a rendering engine which they 开发者_运维百科can draw/code the images and we set the style parameters: line, colour, etc... But to pursue this option I want to experiment myself.

Edit: great responses thanks. The aim is to make something along the lines of http://hascanvas.com/ if anyone is interested.

Thanks Ross

---

Mandelbrot set, Julia sets, random graphs, Lorenz attractor.

Maybe minimising energy functions on a sphere.

---

I'm quite sure that I don't fully understand what you are after, so to provoke you and others into clarifying, I suggest you grab a copy of Mathematica and of Web Mathematica and knock your clients out with that.

---

Mandelbulb.

---

Fractals

with pseudo code.

---

You can have a look at these links:

• https://mathshistory.st-andrews.ac.uk/Curves/
• https://www.nctm.org/classroomresources/
• https://planetmath.org/famouscurves