#turtle graphics

[blake447]

Now to just get the edges curved so that it looks even more interesting once finished

Code's a bit more of a mess than the dragon curve but it follows the process explained in this post here

[turtle-programming]

Python Turtle Tutorial, #3 Turtle Screen Class ...

The Screen Class and the method "title()"...

Post #12: YouTube, John Philip Jones, Python Turtle Graphics, #3/14 Python Turtle Screen Class, 2023.

[commodorez]

HES Turtle Graphics & Turtle Graphics II

Turtle Graphics for the VIC-20 Turtle Graphics II for the C64

[retrocgads]

USA 1984

[syncos-biggest-fan]

[blake447]

One more lol. Sierpinski Eulerian circuit, colored based on distance along the circuit. Ended up fairly visually interesting

[blake447]

Arcane method of drawing the Von Koch Curve

So, some of you might remember my old post about the dragon curve, and an odd way of drawing that by calculating the nth term as a sum of bits in series of binary sequences. For those that haven't seen it, go check that out, its more understandable I think. Also, note that while this is using turtle graphics, we use absolute heading rather than angles left or right. This means that each term is entirely independent and could be calculated in parallel using multi-threading or even a GPU if for some reason you wanted to.

But Blake, I hear you asking, how do you express the Von Koch curve as a sum of bits in a series of binary sequences. Well, I'm glad you asked! Well, we start by once again assigning modular integers to each of the possible directions required to draw the curve, modular simply meaning that once we go above a certain number (5) we simply rollover back to zero. We call this (mod 6). Once we do that, we examine how we can boil the curve down into a sequence using these numbers. By inspection, we see one interpretation being to start with 0, expand the sequence by a factor of 4, and strike the middle two quartiles out, adding one to the first inner quartile, and subtracting one from the second inner quartile, as shown in the process below

And again as with the dragon curve, we can rearrange the order we do this and propagate the added and subtracted ones, which when following the expansion by a factor of four forms alternating patterns. Now from some information theory, since we have positive and negative ones to represent, we need two bits in order to represent the each term in the series, hence the two bit sequences.

Unlike last time, I've actually formalized this a little bit. Here is the derivation for the rules on generating arbitrary sequences of power of two times repeating 0's and 1's, with the ability to offset the start of the sequence, as was necessary with the dragon curve.

Now we can take that formalization, do a bit of inspection of the sequences necessary to compose the adding / subtracting pattern, and derive a series formula that calculates the nth term of this manner of representing the Von Koch curve

Finally, now that we have our series representation, we can modify our original dragon curve code and generate a Von Koch curve after we've translated the series into computer instructions. Note that powers of 2 turn into bit shifts of 1, and indexing requires bit shifting the value and bitwise and-ing with 1 to get the desired bit, calculate the length of the sequence on the back of an envelope aaaaaand....

Holy shit it just worked?... I mean voila! It uh, it draws a koch curve. With the bonus that this code is entirely un-fucking-readable unless you're insane, like me. But yeah, really having fun with this binary sequence stuff because its cool as hell.

[blake447]

A Chaotic way of drawing an Eulerian path along Sierpinski's triangle

Been posting a bit about generating sequences for various fractals that draw them utilizing absolute heading turtle graphics. Here's a time lapse of one of said sequences (10x speed) drawing it in perhaps one of the most chaotic methods I think I've seen.

That'll be enough on this topic for now unless I find something really, really interesting but yeah, this has been on my todo list for awhile now