Iterative Tangents

A curiosity journal of math, physics, programming, astronomy, and more.

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Recent posts

Lindenmeyer fractals by LLMs
Gravity on a toroidal planet
Probability of multiple numbers with doubled digits
Probability of repeated digits
Probability of doubled digits

Posts by topic

Fractals with Lindenmeyer systems

Lindenmeyer fractals as data
More Lindenmeyer fractals
Generating Lindenmeyer systems
Improving generated Lindenmeyer rules
Lindenmeyer fractals by LLMs

Toroidal world

Toroidal world
An Earth-sized torus
Torus with Earth's surface area and volume
Toroidal poles
Toroidal interior
Day and night in the toroidal interior
Compass directions on a toroidal world
Map-making on a toroidal world
Gravity on a toroidal planet

Probability

Probabilities on U.S. presidential elections
Multiplying the expected value of a uniform distribution
Adding expected values of uniform distributions
Probability of doubled digits
Probability of repeated digits
Probability of multiple numbers with doubled digits

Taxicab geometry

Taxicab geometry
Ellipses in taxicab geometry
Point-line distance in taxicab geometry
Parabolas in taxicab geometry
Hyperbolas in taxicab geometry
Conic sections in taxicab geometry
Circumcenters in taxicab geometry
Angles in taxicab geometry
Angle bisection in taxicab geometry
Parallel line construction in taxicab geometry
Ovals of Cassini in taxicab geometry

Geometry

Circles on a hypotenuse problem
Hour and minute hand alignment
Right triangle legs

Apps

Astronomical wall calendar
Tiny annual calendar
Tiny calendar redux

Miscellaneous

Squaring double-digit numbers mentally
Retro line art produces quadratic Bézier curves
The 120 years of Genesis 6:3
Lines dividing lines
Random self-intersecting designs
Self-intersecting designs
Bike gear ratios
The Palenque Code
Four-function calculator behavior
Spirals from ellipses
Retro line art
Bus barn dequeueing
Calculator words
Drawing the Mandelbrot set
Semi-tessellation with a continuous line
Mid-oceanic ridge trace
Scaling stars on the flag

Stack-based mental math

Stack-based mental math
Improving a mental math stack algorithm
Rewriting stack algorithms programmatically
More flexible rewrite rules
Chunking stack-math operations
Stack-based square and cube roots
Stack-math compendium
Stack math revisited
New stack math compendium

Reflections

Mini Zettelkasten
Adventures in notebook programming
On RSS
Counting on my fingers
Song recursion
HTMX versus ClojureScript
Boolean flags hide two functions in one
Implicit stack climbing
An advantage of Python comprehensions
Blogging deep dives
Read and write optimization of notation systems
Refactoring in different domains
Most compelling form

Clojure

quick script for Vim and Tmux
quickbb script for Babashka
Babashka script to serve stdin
Clojure-flavored JavaScript
A Clojure reader with string interpolation
Nelson rules
Scraping an HTML dictionary with Babashka and Bootleg
HTTP server that watches files
Tips for long-running nREPL jobs
Mapping regex matches
Topological sort in Clojure
Manipulating SVGs in Clojure
EDN data DSL
Clojure radix literals
Stacking Clojure's "ignore next form" reader macro
Clojure indentation commas
Updating requires with rewrite-clj
Refactoring Instaparse trees
Babashka scripts to notify on stdin
Improved re-map

Shorthand

Shorthand
Gregg resources
Grascii generation
Handling stacked Grascii affixes
Handling multiple Grascii options

Workflow

Vim syntax range plugin
Clojure scratch files
Conjure plugin for Neovim
Exploratory testing on pull requests
Drafting pull requests

Tmux

Tmux as development environment
Tmux session launcher
Tmux worktree scripts
Tmux session finder
Tmux window launcher
Get last command output from Tmux

Penny game

The Penny Game
Penny game work in progress
Productivity improvements in the penny game
Constraining input in the penny game
Constraining input based on the current state
Utilization in the penny game
Time to completion in the penny game
Animated penny game
The penny game and Kingman's formula

GeoJSON

Geojson.io
Merging GeoJSON features

Sunrise & sunset

Rotation of the solar terminus
Sunrise, sunset, and the winter solstice
Sunrise, sunset, and latitude
XKCD's "Summer Solstice"
XKCD's latitude

Programming

Live reloading HTML that didn't ask for it
Live reloading Tampermonkey scripts
Niche refactoring

Musical temperament

Musical temperament
Matching just intonation to equal temperament
Ratios between semitones under just intonation

Janet

Insta-parsing with Janet
Generating EDN from Janet

Calendar math

Calendar recurrence
Doomsdays
Calculating anchor days
Calculating a date's day of the week
Month recurrence
Recurrence intervals near non-leap year centennials

Clojure macros

ClojureDart macro for nested components
Simple macros
Debugging macros
Logging macros

Earth geometry

Distance to horizon
Horizon distance along ground
Apparent size above horizon
Sunlight's distance through the atmosphere
Great circle distance formulas

"A Walk in the Sun"

A shorter walk in the sun
Nuances of a shorter walk in the sun

Obb scripts

Obb script to copy browser URL and paste Markdown link
Obb script to create new Obsidian file from browser URL
Obb script to execute JavaScript in an open browser

Elliptical orbits

Mapping elliptical orbits
Mapping orbital positions
Orbits with the same period

Logic puzzles

Sum and product puzzle
Sum and product puzzle extra credit
Locker doors puzzle
DogBunny puzzle solver

Fennel

Neovim with Fennel
Hammerspoon with Fennel

Speeding analyses

Saving time by speeding
Speeding and stop lights
Speeding and traffic
Choosing a speed to minimize passing
Driving fast but not fastest

Mnemonics

Finding mnemonics in a body of text
Major system mnemonics
Phonetic major system mnemonics
Constructing major system mnemonics with grammar
Major system mnemonics with a smaller vocabulary
Constructing major system mnemonics with Markov chains

Identicons

Hand-drawn dungeon identicons
Divisibility graph identicons
Symmetrical identicons
Superformula identicons

Clojure transducers

Transducers
Workaday transducers
Specialty transducers
Exponential smoothing transducer
Lens transducer

Jumping higher

Jumping higher when the sun is overhead
Jumping higher when the sun and moon are overhead
Jumping higher when the sun is overhead on different planets

Divisibility graphs

Divisibility graph for 7
Divisibility graphs and modulo tricks
Modulo tricks in other bases
Best base for modulo tricks?
Divisibility scatter plots

Island generation

Basic island generation
Coastal variation
Recursive subdivision

Taskmaster hiding strategies

Hiding strategies
Probabilities when hiding more items
Finding hide and seek probabilities analytically

Gantt charts

Relative schedules
Gantt charts of diverging possibilities
Uncertain Gantt
Timeline of the patriarchs

Slowing population growth

A sigmoidal population
Growth limited by interpersonal conflict?

Nomography

Rate, time, and distance nomogram
Manipulating nomographic matrices symbolically
Rate, time, and distance nomogram for shorter distances

Relativistic physics

View from a photon
Accelerating to oblivion?

Michigan

Michigan county boundary roads
Michigan big trees near you

Drawing an icosphere

Drawing an icosahedron
Drawing an icosphere

Heating cold water

Heating cold water
Modeling a simple thermodynamics problem
Heating cold water in smaller batches
Analysis of incremental water heating

Random hand-drawn checkerboards

Procedural generation by hand
Variations on hand-drawn dungeons
Terrain chess
Checkerboard islands