A little toy I spent too much time on, just because fractals are always such catnip for me.

The LÖVE app with all its source code if anyone wants to play with it.

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I spent several hours trying to debug my notebook app last night, getting increasingly frustrated and demoralized. Eventually I realized there's a bug in my parser. It's a drag having to redo something I thought I was done with.

This morning I went back and built a debug UI for the parser, and now it shows the bug at a glance. The parse tree in the background is for the line the mouse pointer is hovering on.

I need to learn to switch gears more quickly from:

"This should be easy, I suck."

to:

"I'm having trouble with this, it must be hard."

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One fun thing is the couple of lines in the middle there. I reached for a notebook to scribble some equations for myself, but then realized all I wanted was to be able to draw the fraction line horizontally -- and I'm sitting in a tool that can do that. Using the tool to debug the tool :boom: (At least until I have no tools because I broke my tools using my tools.)

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Adding styling to my notebook UI.

It looks like I care about always making the styling very transparent, so it's possible in principle to guess what characters one needs to type to copy the look of something one sees on screen. So the style directives will never be hidden.

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Very initial draft of a notebook UI.

There are 2 kinds of lines here:

• Regular lines are prose, but you can also insert named blanks into them using the syntax [value|name], which renders vertically across 2 lines. You can't nest blanks within blanks. These lines can wrap, but a single blank can't wrap across multiple lines on screen.
• Indented lines (though the indentation is currently subtle) are code. They can render fractions using the syntax (a/b) as I showed before. (Not sure I'll keep this in the long term.) You can nest fractions within fractions. These lines don't support wrapping.

Planned:

• synchronizing blanks with the same name
• using code in indented lines to compute derived names without values inline

Inspirations:

• Kragen Sitaker's bicicleta
• Jonathan Edwards's Subtext 1

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I've implemented the Mandelbrot set several times before, but zooming manually into the Mandelbrot set on a touch screen is surprisingly delightful.

Get it from the Lua Carousel Devlog.

It takes only 20 lines of code to implement the core of the Mandelbrot set. But then it takes 20 lines to specify the palette. And 100 lines to adjust the viewport in response to touch events. And another 10 lines to render at lower precision while touches are in progress.

This does run into the limits of floating-point precision at some high level of zoom.

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My Sokoban client now includes the Microban puzzle sets.

"Sokoban puzzles crafted with the express aim of being tiny, tight and foundational for Sokoban idiom.. Effortlessly teaching you an entire language of mechanics through focused and methodical exploration of a ruleset." — a nice 2-minute video review

Download: sokoban.love

How to switch to the Microban levels:

(Or play them in a non-mobile web browser at Sokoban Online.)

(Microban is by David W. Skinner.)

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While I recently made text2.love easy to embed in other LÖVE projects and documented its API, the true interface of this thing doesn't lie in how you wire it up its bog-standard handlers. No, it's what you do in a workhorse internal method called I.get_rect which gets called on every frame and for every input event.

Here's a very silly example of the sort of app that is now easier to create:

Repo
Compare with text2.love

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Max Bernstein and I have been playing with and putting together a rudimentary 0-dependency cross-platform platform for GUIs. Standing on the shoulders of Fenster and microUI, 2KLoC to support Linux, Windows and Mac without any SDL. (No shade on SDL, though.)

Here's a longer blog post by Max.

Repo

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Now that I have a nice design for a text editor widget, I've been putting it through its paces, particularly for ideas like syntax highlighting and something I call "syntax geometry". Here's a kinda whimsical toy where '+' flips the direction of writing from horizontal to vertical and vice versa.

I only had to put this rule in in one place, and all my support for editing, moving and clicking on the screen to position the cursor continues to work.

(I did need to generalize a couple of things to get to this point.)

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The patterns of Barricelli

I've been obsessed recently with the work of Nils Aall Barricelli who pioneered cellular automata 15 years before John Conway, artificial life 20 years before Christopher Langton and chaos theory 15 years before Benoit Mandelbrot. Barricelli called his creation "symbioorganisms", but it's interesting to try to demystify them without any analogies with living organisms.

The playing field is a finite, circular 1D space of discrete squares. Squares can be occupied by one of many different kinds of elements. Each kind of element has a propensity to move through the space with a constant step. To this space of elements striding around, Barricelli adds 3 rules. (Well, he experimented with many different tweaks in his papers, but this is one concrete, elegant formulation.)

• Destruction: When two objects collide, delete both. (This isn't quite what Barricelli says. But it suffices!)
• Creation: When an object A moves to where a second object B used to be, make a new copy of it, somewhere nearby that depends on B.
• Mutation: This rule is slightly more difficult to explain, and I found the rules plenty interesting without using it in this post. In brief, empty squares sometimes create new kinds of elements.

Just adding the first 2 rules gives rise to some very interesting behavior. Here's a pretty picture:

In this picture, each row of pixels represents the state of the space at one point in time. Time moves from the bottom of the picture to the top. The space is seeded randomly with a few different kinds of elements. Elements that stride rightward are colored shades of green. Elements that stride leftward are colored shades of blue. Red pixels are empty squares.

This picture shows that at the start we have a lot more differences in color, but in a few generations the "populations" (coherent bands of color) quickly become more stable.

Zooming in, we see that what looks like flat shades of color are really extremely regular patterns of the different kinds of elements. These are Barricelli's "symbioorganisms".

How could this be? The different colors of elements stride in different directions at different rates. How do stable patterns emerge? Here's one example that shows what's going on:

Here I've annotated the zoomed-in view with each element's stride, and lines showing each element's motion. The blues (B) move 3 squares left per time step, while the greens (G) move 2 steps right. However, a configuration of BBGGG is stable with just these rules. Each pair of blues "switches partners" with a different triple of greens going the other way. The effect is of a stable periodic pattern with a period of 5 squares.

I've tried many different random initial conditions, and such periodic patterns always occur. Barricelli calls this phenomenon "spontaneous generation", and it is remarkably robust. The BBGGG pattern above is nowhere near the only possible organism. Another simple one is BBBGG:

Very similar phenomenon of groups of like elements "switching partners."

One example that suggests why these patterns robustly occur is to introduce a single empty (red) square into a field of BBBGG. What we see is the empty square "move" leftwards at a rate of 3 squares per time step — and it leaves to its right a growing field of BBGGG. Similar effect to a catalyst or enzyme.

The consistency with which periodic patterns occur is largely due to the balance between creation and destruction rules. Here's a different and much more complex periodic pattern elsewhere in the same space:

This is a complex pattern with a period of 25 squares, and for its stability it requires both destruction (places where the white lines of movement intersect, annihilating colliding elements) and creation (red lines that cause a square to create a second copy of itself).

Open questions

• I haven't dug into the third rule (mutation) yet to understand its effects in detail.
• Barricelli describes complex organisms arising from a random field of just +1s and -1s (i.e. elements striding 1 element leftward or rightward), but I have a simple proof that that can't happen with the rules as I've described them above. I'd like to understand how to tweak the rules to reproduce this result.
• Barricelli describes patterns that aren't stable by themselves, but can spread in the presence of "host patterns". He calls these parasites, though it may be more precise to compare them to viruses. I'd like to reproduce some of the patterns he mentions.

Philosophical aside #1

One interesting claim Barricelli makes (pg 2): a pattern that reproduces itself tends to also propagate the environment that it arose in. If something about the environment caused an organism to spontaneously arise, almost by definition the organism is required to preserve that property to reproduce itself. So he claims that the insides of cells likely are very similar in some ways to life on earth back when RNA spontaneously emerged. No way to be sure, of course, but the argument kinda hangs together for me. And the empirical evidence for this is that the Earth is 4.3 billion years old, and life on the earth is around 4 billion years old. Once conditions were right, life basically emerged in a cosmic eyeblink. One way to view all of later life is as ways to protect that initial environment in the face of more and more hostile environment changes, to create little bubbles of the primordial soup inside us all.

And it's fractal. As new structures arise to protect old bubbles, they are themselves self-propagating and they need their own environments preserved.

A specific property of the environment isn't necessarily helpful to all life. One organism may need some environmental property that another organism finds utterly hostile. Just by being first, an organism will tend to propagate the environment it needs. And by doing so it's competing with even the possibility of other organisms that don't exist yet.

This line of thought leads me to wonder if it may be easier than I thought to find new conditions suitable for the emergence of life. I know physicists run large simulations of the early universe on supercomputers, which generate plausible compositions of elements over time as supernovas occur. I also vaguely remember from TV programs long ago that we've tried to run simulations of earth's primordial soup using best guesses of its early composition. What if we put these two ideas together? Given a simulation of the early cosmos, generate candidate stars, candidate planets around those stars, plausible initial distributions of elements on those planets, conditions of temperature and pressure. Then simulate brief slices of time. If (my interpretation of) Barricelli is correct, life either emerges instantly or not at all, and we may be able to try out a variety of conditions relatively cheaply. And maybe identify candidate chemistries that help molecules reproduce.

There's probably some professor somewhere who is aware of past research in this vein and can point me at papers :)

Philosophical aside #2

One way to view the story of our evolution is as a leveling-up of goals:

• Life: "cells maintain the environment in which RNA molecules originated."
• Bureaucracy: you create a system that can outlive you. The system outlives its own usefulness.
• Permaculture: design systems to try to make themselves less and less necessary to the functioning of the ecosystem.

Credits

Some example code from Simone Conradi and some pointers to literature from Karsten Schmidt got me going. This paper was my primary source.

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