Using Animation Nodes with the expression node with equation starting with x(n+1)=

Question

I'm trying to animate the variables for various strange attractors using animation nodes and it's expression node.

The equation I'm trying to animate.

I can create the equations and animate the a variable in Octave / Matlab (but as you can see it's not a great image see animated gif below nor does it have the "whispy shear stocking" look).

I originally thought of using Blender 2.8 and using a python script. See original question:

Then realized that animation nodes has an expression node that may make it easier to animate and allow the changing of the expressions without knowing how to code python. Video Tutorial

I can create part of the expression but I'm not sure how to get the Xn+1, Yn+1 values to work with the expressions node.

Background on the Clifford attarctor. Some more info with Python code

I've attached a blend file with a working parametric Epitrochoid equation. I'm just not sure how to get it to work with the Xn+1 and Yn+1 values

I'm using Blender 2.8 in Ubuntu 18.04 running Animation Nodes 2.1.4

Answer 1

It is like an iterative process to calculate the equations you have mentioned in your question. Thus, at step 1 (n = 1), we supply some initial value for (x, y) say (x0, y0) and calculate the equations or (x1, y1) then in step 2 (n=1), we will use the previous (x1, y1) to calculate the equations (x2, y2), and so on. Therefore, we have to store the calculated value of (x, y) during each iteration step.

In animation nodes, the loop node has feature is called Reassign (see Advanced Node Settings in the N-panel) to store data per iteration that we can use in the next iteration. In this image, I have reassigned (or reinitialize) the vector input that acts as x(n), y(n) for the next iteration i.e., x(n+1), y(n+1).

Then animate the (a) parameter using Animate Float Node,

Here is Blend File: