An Excited Time Drawing Mandala Fractals Today (2023-04-06)

An Excited Time Drawing Mandala Fractals Today 2023 04 06

Today at this moment, I was thinking about fractals and mandalas. I’m always thinking about these concepts, but I just got excited about it and stayed playing with some drawings I figured out.

It’s a way to feel better, that I’m doing what I love, I just had to do it even though I had no schedule for that.

Among being a mathematician, engineer, philosopher, entrepreneur, gamer, and others…, being an artist who designs the meaning of all this knowledge is part of my stance.

I’ve wished to formalize the MathSwe logo, so it can be defined declaratively via recursion or an elegant equation instead of Photopea 1 vector shapes or raster graphics.

So, I’ve been playing with some recursion and fractals once in a while the last few days.

One example is the below drawing with animation I was checking last time:

Basic Fractal with Circles
Basic Fractal with Circles

It was just a basic PoC, and I got some insights, for example: recalled that understanding the constant part of relativity and recursion is a key to understanding relativity, and that, as the radius gets bigger the circle looks relatively “flat” but it’s still a circle, so you can use your imagination or creativity which is another key and think that “you’re getting closer to the surface of the sun”, so many will believe that “the sun is flat” because that’s what they see in their local, fragmented, or absolute perspective but as we understand relativity we know what’s happening, and that these shapes are circles (relatively).

Notice how recursion contains that constant part of relativity: the recursive function is the pattern that keeps constant (one part), and the observer is the domain of the function that keeps changing (second part).

That sounds familiar, it’s like induction (so math). Base step, recursive/inductive step.

That is, mathematical elegance with homogeneity, as I say in From Imperative to Functional: TypeScript Fetch Promise, the simplest designs are the best, and homogeneity yields the simplest form of a problem so that the other part can constantly keep changing peacefully. That’s also a way to see and prove how boilerplate is a measure of bad quality of software, you have to factorize it.

Now, the drawings I was playing with today were about circles and a version of the Sierpiński triangle.

I drew 2 a flower petal as a base for the drawing, and put some triangles as source-atop composite operation. I made them smoother with arcs, so they’re smooth curves instead of ugly lines with discontinuities 3 as plane triangles would otherwise be. I added some colors to the shadows, etc.

It’s not perfect, and not symmetric, but it’s a pretty nice and valid result.

It was an improvised drawing, out of passion and curiosity to relieve the stress of these days.

I liked it a lot, the shapes, the colors, the experience, it was lovely.

I also learned about what particularly “mandala fractals” are since they’re a specific type of mandala drawings that use fractals and are created using computer graphics, so it’s convenient for me to work with them, because of the fractal and computing part they consist of.

Right now, I’m not providing source code or projects regarding these drawings, but a lot is coming to Repsymo and MathSwe.

I’ve also thought about automating the creation of this kind of content, so I already have a mature idea of what to do.

It was good to have worked with drawings, mandala fractals, and ideas these days as they gave insights, and relaxation, I’m closer to fulfilling some objectives about MathSwe and Repsymo, and I’ll keep doing this great job.



  1. Photopea is a free version of Photoshop 

  2. I’ve been using HTML Canvas lately for this 

  3. For me, mathematical beauty lies in smooth curves with continuous derivatives