Roessler

1. roessler, a library which solves the differential equations producing the Roessler Strange Attractor.

2. lazytrig, a transcendental functions library, providing sine, cosine, logarithm, exponential, etc., in @rs.

3. proj-3d, a generator which takes the 3D coordinates produced by roessler and produces either a list of 2D points or a full 2D PPM image.

These programs are available for use on Urbit under the MIT License.

Novel Features

1. Differental Equation Solver. I created a Runge-Kutta fourth-order differential equation solver, ++dxdt:roessler and variants. These are currently hard-coded to the Roessler calculations at ++xf:roessler etc. but are flexible for any other appropriate gates.

   Example Usage:

   /+  roessler
   ::  Render 1,000 3D points at a dx of 0.01.
   (genxyz-pts:roessler 1.000 .0.01)
   

   Example Output (100,000 points rendered with Python):

   

2. Transcendental Functions Library. I wrote a series-based mathematical functions library to support proj-3d. It is unjetted, but supports sine, cosine, tangent, logarithms, arbitrary powers, and exponentiation.

   Usage:

   /+  lazytrig
   ::  Calculate sine(pi/4)
   (sine:lazytrig (div:rs pi:lazytrig .4))
   

3. 2D Projection of 3D Points. I implemented the matrix mathematics necessary to convert 3D points to a 2D plane with perspective view. (Alas, using only lists of lists of @rs as the linear algebra library is developed independently.)

   Usage:

   /+  roessler
   ::  Render 1,000 points at a dx of 0.01.
   (genxyzs:roessler 1.000 .0.01)
   

4. In-Urbit Rendering of 3D Points. I implemented a PPM rendering which creates a black-and-white image of the 2D points.

   Usage:

   ::  Render a 1,000×1,000 image of 10,000 Roessler points.
   (gen3d-ppm (ravel-3d-pts (gen-3d-pts 1.000 10.000) 1.000))
   

   or

   *%/web/output/txt +proj-3d [1.000 10.000]
   

   Then convert the txt to ppm and clean up Hoon syntax artifacts (like .0 for 0).

   Output (PPM file converted to PNG):

   

Here's a GIF generated from a few camera views about the origin.