A few days ago I posted some grids made by taking Delannoy numbers mod something
Delannoy numbers have application for determining how many distinct constrained walks you get of a certain type in grids of various sizes
Here we constrain to → ← ↓ ↑
I don't forbid backtracking
Guilloché patterns, formed by adding a little offset into parametric curves involving sines and cosines to create a dense overlay of curves
It gets used a lot for security features on money because a small change in parameters produces a large detectable change in result
So, a kind of pseudo-asemia here: bills from the Bank of Mary
(Shows better on screen if you expand)
θ[n+1] = (θ[n] + 2πs) mod (2π)
φ[n+1] = θ[n] + φ[n] mod (2π)
θ = φ = 0
s = irrational number
Draw unit line between iterations
A parametric l-system may not be the most efficient way to do this, but it was the readiest to hand in the moment...
Multi-level Turing patterns, per McCabe (http://www.jonathanmccabe.com/Cyclic_Symmetric_Multi-Scale_Turing_Patterns.pdf)
Achievement unlocked: parameteric L-system implementation
That, plus a WHOLE lotta refactoring, clean-up, and realignment of the L-system APIs in the next release, coming soon
(Aside: it is annoying that Mastodon puts a black background for edit/preview on images w/ no background colour even in light mode.)
What if you applied the sin(sin(sin... trick to complex numbers?
1: decide what to do about results that get too large. I've played with various routes here: normalizing everything (BO-RING), reusing the value from the previous series, skipping bad values from plots
2: Running parametric function over t (double) what complex to use? t+ti? t+0i? t+i?
Here, Darth Vader is t+i, sequential constants, all sin, skip from plot
What if you plotted sin(t) and then sin(sin(t)) and sin(sin(sin(t)) and ...
What if you introduced constants, e.g. sin(2 sin(t))?
What of you mixed it up a bit and sometimes used cos instead?
Here's using Pascal sequence (with mod + 1) for constants and random sin/cos
Given the recent influx, an #introduction
My background is #mathematics and #linguistics w/ eclectic interests. Sometimes attend/livetweet #astrobiology conferences just for fun. Spent career in #software (server-side #search #IR #database). Put in lotta miles on markup standards (#XML #XQuery).
Retired now, writing programs to make #GenerativeArt, post some here.
Lots of curmugeonly opinions, which I sometimes share
Music as a pattern-generator
I like the idea of music as a source of patterning for generative art: not quite regular, not quite random.
This bit of madness turns a musical score into a noise field by mapping the measures into a grid. The value of the function is based on the scaled pitch for the notes at that point in the grid. Values mapped to colour range.
Gloria from di Rocco's Mass for Pope Benedict, with the parts aligned.
The weird and wonderful world of continued fractions
The square root series (√j) with log colouring, using 0 for finite sequence terms, one line per j
The black bars are for the perfect squares 1, 2, 4, 9,... whose continued fraction (as with all rational numbers) terminates. Not sure what to make of that regular line of red dots for√22
Newton #fractal of the day
Smoothed iteration colouring; "bukavu" gradient (a split topographic gradient, which is why you get hard boundaries from dark green to light blue; the sharp green-green lobes are not such artifacts)
Yes, it was a bug that made all the coefficients the same, but it turned out pretty for all that
The basic chaos game uses random vertex selection, perhaps constrained (e.g."don't pick the same vertex twice in a row").
I experimented w. integer sequences of various sorts, e.g. the Fibonacci, which you take mod the #vertices. If you just use the first N numbers of this sequence repeated, and N < #points, interestingly, you only get N distinct points plotted!
1/φ, regular pentagon: inventory, Recaman
The chaos game (https://en.wikipedia.org/wiki/Chaos_game)
Map point to new point some fraction of distance to vertex of a polygon. Iterate. Depending on fraction, polygon, & constraints on which vertex you pick, you get different results, some of which are fractal in nature.
√5, regular pentagon, if two vertices in a row are the same, you can't pick one of the adjacent vertices (blue)
0.5, regular pentagon, you can't pick the same vertex twice in a row
Well, here's a bit of a head scratcher, and I'm open to any suggestions of where to even begin to look: I have a test (#XSL run by #Saxon with Java) that works perfectly well when run on the command line, but not when I put that command line in a make file. For that matter, a completely identical test in #XQuery runs perfectly well in both cases.
The failure mode is "impossible": an assertion that two values are the same fails, but the error stack shows them to be, in fact, the same.
So... you haven't seen my #GenerativeArt interludes in some little while. I've been busy with my quixotic quest to run some my art code under #SaxonJS, which meant porting from #XQuery to #XSL, which meant making some tools to do that because I am that kind of lazy, which meant figuring out how to do Saxon Java extension functions, but! Mirabile Dictu, it works. It all works... except... I have some odd performance issues that only happen in SaxonJS that I'm having narrowing down. Disappointing.
#Genuary day 26: My kid could have made that
I set about to make something in the style of one of my daughter's old drawings, capturing some of the childish imperfections. Getting it sloppy enough but not too sloppy is pretty hard. Also, she has a much better sense of composition and colour than I could capture. (Original on left.)
Genuary day 21: Persian rugs
Well, not so Persian, perhaps, but I like them. The weavings are driven off randomly selected integer sequences, with one driving the initial row, one driving how that evolves row by row, and one driving colour shifts.
Two stars dancing
#genuary2022 Day 2: made in 10 minutes
Recently cleaned up/refactored some of my coordinate mapping and curve plotting code; so grabbed some test code and added a small amount of parameterized randomness.
Here: Bipolar mapping of At sin(Bt) / Ct cos(Dt) for some mutually prime A, B and C, D
Given z[n+1] = f(z[n]) for some complex function f, count how many iterations it takes for the function to escape to infinity (really: some suitably huge number) and map that to colours.
Here cubic + c/quadratic:
f = (0.79z³+0.97z²+0.79z+-0.8)+(-0.37+0.12i)/(5z²+3z+-4)