@thi.ng/complex

[!NOTE] This is one of 201 standalone projects, maintained as part of the @thi.ng/umbrella monorepo and anti-framework.

🚀 Please help me to work full-time on these projects by sponsoring me on GitHub. Thank you! ❤️

• About
• Status
• Installation
• Dependencies
• API
• Authors
• License

About

Array-based complex number algebra.

Status

ALPHA - bleeding edge / work-in-progress

Search or submit any issues for this package

Installation

yarn add @thi.ng/complex

ESM import:

import * as com from "@thi.ng/complex";

Browser ESM import:

<script type="module" src="https://esm.run/@thi.ng/complex"></script>

JSDelivr documentation

For Node.js REPL:

const com = await import("@thi.ng/complex");

Package sizes (brotli'd, pre-treeshake): ESM: 1.03 KB

Dependencies

• @thi.ng/api
• @thi.ng/checks
• @thi.ng/math
• @thi.ng/vectors

Note: @thi.ng/api is in most cases a type-only import (not used at runtime)

API

Generated API docs

ASCII art mandelbrot fractal using complex number math

import { abs, madd, type Complex } from "@thi.ng/complex";
import { SHADES_ASCII_16, canvas, formatCanvas } from "@thi.ng/text-canvas";
import { map, range2d, run } from "@thi.ng/transducers";
import { fit2 } from "@thi.ng/vectors";

// mandelbrot evaluation
const mandelbrot = (pos: Complex, escapeRadius: number, maxIter: number) => {
    let i = 0;
    for (
        let z: Complex = pos;
        ++i < maxIter && abs(z) < escapeRadius;
        z = madd(z, z, pos)
    );
    return maxIter - i;
};

// text canvas setup
const canv = canvas(120, 60);

// evaluate for all pixels and visualize as ASCII art
run(
    map((pos) => {
        // compute fractal at pos
        const m = mandelbrot(
            // map pixel pos to mandelbrot region
            fit2([], pos, [0, 0], canv.size, [-2, -1.25], [0.65, 1.25]),
            // escape radius
            2000,
            // max iter = number of chars/shades
            16
        );
        // set pixel using corresponding shade
        canv.setAt(pos[0], pos[1], SHADES_ASCII_16[m]);
    }),
    range2d(...canv.size)
);

// output canvas as string
console.log(formatCanvas(canv));

XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG33333333333333GGGGGGGGGGGGGGGGGGGGGGGGGGGXXX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG3333333333333333333333GGGGGGGGGGGGGGGGGGGGGGGGGX
XXXXXXXXXXXXXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333lllll333333333333GGGGGGGGGGGGGGGGGGGGGGG
XXXXXXXXXXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333llli=iiilllll3333333333GGGGGGGGGGGGGGGGGGGG
XXXXXXXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG33333333333333lllii+-,+iiilllll333333333GGGGGGGGGGGGGGGGGG
XXXXXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG3333333333333333lllllii=:  +=====illl3333333333GGGGGGGGGGGGGGG
XXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG33333333333333333llllllii==+-  --,,,=illll3333333333GGGGGGGGGGGGG
XXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333333333llllllliii==++:,   ,:+=iillll33333333333GGGGGGGGGGG
XXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333333333lllllllliiii==++:,    ,:+==iilllll33333333333GGGGGGGGG
XXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333333333llllllllliiii==+, ,.      ,:::=iillllll33333333333GGGGGGG
XXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG3333333333333333333lllllllllliiiii=+-              -+=iiilllllll3333333333GGGGG
XXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG33333333333333333333llllllllliiiiiii===+:-             -+==iiiillllllll33333333GGGG
XXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333333333333llllllliiiiii======++::              -:+===iiiiiiillllll3333333GG
XXGGGGGGGGGGGGGGGGGGGGGGGGGGGG3333333333333333333333llllllllii===++:+++++:::--,            .-:::++====iii===illl3333333G
XGGGGGGGGGGGGGGGGGGGGGGGGGG3333333333333333333333llllllllliii=:     ,-:-,                     ..   +++++++- -iill3333333
GGGGGGGGGGGGGGGGGGGGGGGG33333333333333333333lllllllllllliiii==:        .                           ,-- .-,. -:=ill333333
GGGGGGGGGGGGGGGGGGGGGG33333333333333333llllllllllllllliiiii==+:-                                             :=illl33333
GGGGGGGGGGGGGGGGGGGG3333333333333lllllllllllllllllliiiiii===++:-.                                          .:+=illl33333
GGGGGGGGGGGGGGGGG333333333333lllllllllllllllliiiiiiiiii===+:- ..                                           ,+=iillll3333
GGGGGGGGGGGGGGG333333333333lllliiiiiiiiiiiiiiiiiiiiii====+:                                               .-+==iilll3333
GGGGGGGGGGGGG333333333333lllllii: -+===================++:-,                                                -:++=illl333
GGGGGGGGGGG3333333333333lllllii=+, :+++++++: -++++++++++:-,                                                     +illl333
GGGGGGGG33333333333333lllllliii=+- .., ,---   ,---::::::-,                                                      +illl333
GGGGGG3333333333333lllllllliii==+:-,              .,----,                                                    .:+=illl333
GGGG3333333333333lllllllliiii===+:-.                 ...                                                      ,:=illl333
GG33333333333llllllllliiiii===++:-,.                                                                           +iilll333
333333333llllllllllliiii==:+++::,                                                                            .+=iilll333
333333llllllllliiiiiii===+- ,,,..                                                                            -=iillll333
333llllliiiiiiiii======++:-.                                                                                :==iillll333
llliiiii==:-+++++:++++:.,,                                                                                ,:+=iiillll333
                                                                                                         ,:+==iiillll333
llliiiii==:-+++++:++++:.,,                                                                                ,:+=iiillll333
333llllliiiiiiiii======++:-.                                                                                :==iillll333
333333llllllllliiiiiii===+- ,,,..                                                                            -=iillll333
333333333llllllllllliiii==:+++::,                                                                            .+=iilll333
GG33333333333llllllllliiiii===++:-,.                                                                           +iilll333
GGGG3333333333333lllllllliiii===+:-.                 ...                                                      ,:=illl333
GGGGGG3333333333333lllllllliii==+:-,              .,----,                                                    .:+=illl333
GGGGGGGG33333333333333lllllliii=+- .., ,---   ,---::::::-,                                                      +illl333
GGGGGGGGGGG3333333333333lllllii=+, :+++++++: -++++++++++:-,                                                     +illl333
GGGGGGGGGGGGG333333333333lllllii: -+===================++:-,                                                -:++=illl333
GGGGGGGGGGGGGGG333333333333lllliiiiiiiiiiiiiiiiiiiiii====+:                                               .-+==iilll3333
GGGGGGGGGGGGGGGGG333333333333lllllllllllllllliiiiiiiiii===+:- ..                                           ,+=iillll3333
GGGGGGGGGGGGGGGGGGGG3333333333333lllllllllllllllllliiiiii===++:-.                                          .:+=illl33333
GGGGGGGGGGGGGGGGGGGGGG33333333333333333llllllllllllllliiiii==+:-                                             :=illl33333
GGGGGGGGGGGGGGGGGGGGGGGG33333333333333333333lllllllllllliiii==:        .                           ,-- .-,. -:=ill333333
XGGGGGGGGGGGGGGGGGGGGGGGGGG3333333333333333333333llllllllliii=:     ,-:-,                     ..   +++++++- -iill3333333
XXGGGGGGGGGGGGGGGGGGGGGGGGGGGG3333333333333333333333llllllllii===++:+++++:::--,            .-:::++====iii===illl3333333G
XXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333333333333llllllliiiiii======++::              -:+===iiiiiiillllll3333333GG
XXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG33333333333333333333llllllllliiiiiii===+:-             -+==iiiillllllll33333333GGGG
XXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG3333333333333333333lllllllllliiiii=+-              -+=iiilllllll3333333333GGGGG
XXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333333333llllllllliiii==+, ,.      ,:::=iillllll33333333333GGGGGGG
XXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333333333lllllllliiii==++:,    ,:+==iilllll33333333333GGGGGGGGG
XXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333333333llllllliii==++:,   ,:+=iillll33333333333GGGGGGGGGGG
XXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG33333333333333333llllllii==+-  --,,,=illll3333333333GGGGGGGGGGGGG
XXXXXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG3333333333333333lllllii=:  +=====illl3333333333GGGGGGGGGGGGGGG
XXXXXXXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG33333333333333lllii+-,+iiilllll333333333GGGGGGGGGGGGGGGGGG
XXXXXXXXXXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333llli=iiilllll3333333333GGGGGGGGGGGGGGGGGGGG
XXXXXXXXXXXXXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG333333333333lllll333333333333GGGGGGGGGGGGGGGGGGGGGGG
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGG3333333333333333333333GGGGGGGGGGGGGGGGGGGGGGGGGX

Authors

• Karsten Schmidt

If this project contributes to an academic publication, please cite it as:

@misc{thing-complex,
  title = "@thi.ng/complex",
  author = "Karsten Schmidt",
  note = "https://thi.ng/complex",
  year = 2022
}

License

© 2022 - 2025 Karsten Schmidt // Apache License 2.0