I'm a professor of mathematics at the University of North Carolina Asheville. I've also done a fair amount of consulting work over the years focusing on scientific and data visualization.
I'm happy to be part of the first Observable Ambassador's cohort.
Public
Edited
Nov 28, 2022
2 forks
2 stars
p = (1 + Math.sqrt(5)) / 2
full_digraph_input = [
{
// Rectangle in rectangle
source: "R",
target: "R",
f: shift([p, 0])
.compose(rotate(pi / 2))
.compose(scale(1 / p)),
label: "RR"
},
{
// Square in rectangle - don't delete!!
source: "R",
target: "S",
f: scale(1),
label: "RS"
},
{
// Lower left rectangle in square
source: "S",
target: "R",
f: scale(1 / p ** 2),
label: "SR1"
},
{
// Lower right rectangle in square
source: "S",
target: "R",
f: shift([1 / p + 1 / p ** 2, 0])
.compose(scale(1 / p ** 2))
.compose(rotate(pi / 2)),
label: "SR2"
},
{
// Upper left rectangle in square
source: "S",
target: "R",
f: shift([1 / p ** 2, 1 / p ** 2])
.compose(scale(1 / p ** 2))
.compose(rotate(pi / 2)),
label: "SR3"
},
{
// Upper right rectangle in square
source: "S",
target: "R",
f: shift([1 / p ** 2, 1 / p]).compose(scale(1 / p ** 2)),
label: "SR4"
},
{
// Square in square
source: "S",
target: "S",
f: shift([1 / p ** 2, 1 / p ** 2]).compose(scale(1 / p ** 3)),
label: "SS"
}
]
full_digraphIFS = new DigraphIFS(full_digraph_input)
smaller_digraph_input = [
{
// Rectangle in rectangle
source: "R",
target: "R",
f: shift([p, 0])
.compose(rotate(pi / 2))
.compose(scale(1 / p)),
label: "RR"
},
{
// Square in rectangle - don't delete!!
source: "R",
target: "S",
f: scale(1),
label: "RS"
},
{
// Lower left rectangle in square
source: "S",
target: "R",
f: scale(1 / p ** 2),
label: "SR1"
},
{
// Lower right rectangle in square
source: "S",
target: "R",
f: shift([1 / p + 1 / p ** 2, 0])
.compose(scale(1 / p ** 2))
.compose(rotate(pi / 2)),
label: "SR2"
},
{
// Upper left rectangle in square
source: "S",
target: "R",
f: shift([1 / p ** 2, 1 / p ** 2])
.compose(scale(1 / p ** 2))
.compose(rotate(pi / 2)),
label: "SR3"
},
{
// Upper right rectangle in square
source: "S",
target: "R",
f: shift([1 / p ** 2, 1 / p]).compose(scale(1 / p ** 2)),
label: "SR4"
}
// {
// // Square in square
// source: "S",
// target: "S",
// f: shift([1 / p ** 2, 1 / p ** 2]).compose(scale(1 / p ** 3)),
// label: "SS"
// }
]
digraphIFS = new DigraphIFS(smaller_digraph_input)
digraphIFS.show_digraph()
pics = digraphIFS.render_stochastic({ n: 100000, colors: true })
pics[2]
Ancillary code
// Good initiators for the deterministic method
init = [
[
[0, 0],
[p, 0],
[p, 1],
[0, 1],
[0, 0]
],
[
[0, 0],
[1, 0],
[1, 1],
[0, 1],
[0, 0]
]
]
import {
scale,
shift,
rotate,
reflect,
pi,
DigraphIFS
} from "@mcmcclur/digraphifs-class"
MathJax = require("https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-svg.js").catch(
() => window["MathJax"]
)
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