Finding a mini-mand
While running Tierazon version 2.6, I decided to zoom around a little and find something interesting (if I could). I knew that the default max iterations of 128 would never cut it, but I was curious at what point I would need to increase it. Where max iterations became a factor I will show the difference
a. The starting mand looked pretty standard. Here it is (this is actually Tierazon's default which is an M-set with a Newtonian swirl in the middle. I kinda like it):
b. Now that's pretty uninteresting, but I knew there were interesting things to be seen with just a little zooming, so I chose the left side of the mand and came up with this:
c. I know there is something interesting in here somewhere, maybe on the antenna sticking out on the left side:
d. I had seen the dot in the center of the previous frame, but hadn't realized it was a mini-mand. This is getting curiouser and curiouser. Let's take a closer look at that thing:
e. Wow. There's a lot going on in that mand. We're totally off the main mand now, and here is a whole new one to explore. I wonder if they are identical? I look at the starting one again and notice it has much less lightning, or antennae coming off of it. That means there may be something interesting to be seen by zooming in on this one, since there is so much lightning. Let's go in closer:
f. Hey there's lots of detail to be seen here... especially in the antennae. I am curious. What's it look like if I zoom right in at the center?
g. More and more details are visible. That dot in the antenna pointing up and to the left just before it turns into a plus sign looks like it should be a mini mand. Let's check it out:
At 128 max iterations, I could not tell that the shape in the middle was going to be a mini mand. I upped max iterations to 256 when I realized there was detail I was missing, and this is what I saw:
Hey, that shape looks really familiar, so I decided to stay with 256 max iterations for a couple of steps. Why is there a difference? Colors in the Mandelbrot set are selected by counting the number of iterations it takes the function (z^2+c) to become unplottable. In the picture with 128 as max iterations, there is less detail because the program stopped trying to decide what color the pixel should be (and chose the default color which is sort of tan) much much sooner than the one with the 2000 iteration maximum. More and more detail appears when you let the program try harder as you zoom in closer and closer to the objects you want to see. There is a limit to how much more detail will appear with this method. 256 iterations shows nearly all the detail there is to see. After a while, altering max iterations just changes the color of the area that could not be plotted (remember that color is selected based on the number of iterations, so changing the maximum just lets it select a color that corresponds to a different number of iterations than the previous maximum).
Just to make it clear, here is the same region with pretty much the same detail and a change in color at 2000 iterations:
h. OK, back to hunting. Sure enough, more detail shows it wasn't a plus sign to the left of, and above the dot, either, there are 5 antennae. I see the pattern that I didn't realize before. A quick look back to picture f shows that there are 5 antennae (although more complicated) below the dot I chose to inspect. Then, zooming in again, I see that these 5 antenna junctions are all over the place!
I decided to change max iterations again to see if I was missing detail, and this is what I saw at 512:
i. That short upright antenna off the side of the smaller blob bears a closer look:
j. That's an interesting formation between the two biggest antenna junctions on that main spike pointing straight up in the middle of the image. I wonder what that's all about?
k. Hey what is that? I can't tell! Let's zoom some more:
l. It looks like an intense piece of lightning, but there's no mini-mand. Oh come on there has to be one in here somewhere, I am just going to have to zoom in closer. What's that bar going across the middle? Just more lightning? It doesn't look like the rest of the lightning. Zoom in again (image k is already almost 2 million times magnification from where we started):
m. Hey look at that!! There IS something interesting in the middle of that bar going across. I wonder what it is?
n. Looks like I haven't zoomed in enough yet. The suspense is killing me. Good thing these things render quickly at this low resolution (these are all 160 x 120). Let's zoom again:
o. There is something non-lightning about that bit in the middle. What is it?
Hmmm. This looks like a shape I recognize. I wonder if I should just change max iterations to 2000 and get on with the play?
p. Upping max iterations did something, but I need to zoom in more for a much closer look:
q. AHA!!!!!! A nice lil mini with a corona!!! It looks like a little snowflake formed around a bit of chaos :-) Let's go a little closer:
Yep, sure enough, I found what I was looking for, and it's sweet! The interesting thing about it was that it all happened in a matter of minutes. Reading this web page takes you much longer than it took to find this :-) And what rich hunting ground for more minis!!!!!!!! We've already seen that each of those little bars has a mini, so there are countless in this pic alone to go find!!!! A fractal lover's work is never done :-)
Click here or the image to see the full sized rendering of the snowflake Mandelbrot (1024 x 768 24-bit color 289kb).
Click here to see the full size ant-aliased (smoother shapes and lines, really cleans up the corona) version. I would show you a thumbnail, but this small, the anti-aliasing has no effect as reducing the size does much more ant-aliasing than necessary. This image is also 1024 x 768 pixels with 24-bit color. It was rendered at 2048 x 1536 and then reduced by half in the anti-aliasing process.
Click here to see the movie of the zoom. Each frame was rendered at 160 x 120 with max iterations of 2000 and there are a hundred frames at 6 per second. It's not quite smooth, but I wanted to do something that could be downloaded relatively easily. This is a 507kb download, not for the faint of heart, but well worth it for zoom lovers.