This is the monthly newsletter for my fractal animation site, HPDZ.NET. I am sending you this because I think you might be interested.

This is the first newsletter sent via an email service. I am switching to this service for several reasons. If you're interested in the details, read below, or see the explanation I have put on the web site.

If you want to unsubscribe, you can do so immediately, no further questions asked, by clicking here

-- Mike Condron

I usually try to get the newsletter out before publishing stuff to YouTube, but that didn't happen this month due to technical problems learning how to work with the new email distribution service. Sorry!


Canyon2 is finally complete. It is a zoom in to the eastern wall of the Seahorse Valley, or Canyon, where the main cardioid joins the first small circular area on the left. This is the sister video to Canyon1, which zoomed in to the western wall.

Rendering of Canyon2 started on 5-Oct and ended 29-Oct. All together it required nearly 600 hours of computing time to generate the 4800 frames that make up this animation. That's the longest run so far for one of my videos. The final few frames each took over 30 minutes to calculate.

Coloring Canyon2 was more difficult than I had anticipated based on some early test runs. It has the same problems I've described before with Canyon1 and MetaphaseVar1, but worse. I tried literally over a hundred different tweaks to the coloring method and finally settled on something that looks OK but not great. Work continues on this difficult problem.

Using Mathematica, I made a cool animation of the histogram of the fractal data for this animation, and it's showing me some interesting things I had not seen before. I will incorporate these insights into future revisions of the coloring system, and I may come back and recolor Canyon2 if I can make some improvements.

For now, I am reminded of the warning not to let the perfect be the enemy of the good. In this case, the quest for perfection was terminated by the need to get a couple of briskets into the cooker for an overnight run Saturday night. They both turned out great Sunday morning, and for now, this project is moved to the ARCHIVE.

Other News

Math Kernel Updates

I have finally implemented some big improvements to my high-precision multiplication kernel. This is the small bit of code that consumes about 99% of the CPU time when rendering an animation, so any improvements in it can have a huge impact on the time it takes to produce a video. For the software aficionados, here's a summary of the changes:

  • Removal of unnecessary digit multiplications of less-significant digits
  • Elimination of redundant multiplications when squaring a number
  • Loop unrolling for multiplications and carry-save reconciliation
  • Various small tweaks to help cache prediction and pipelining

Some details can be found on a new Technical page.

The result of all this is that the higher precision ranges of arithmetic are running nearly twice as fast as before.

Recursive Subdivision Resurrection

Recursive subdivision (also known as the Mariani-Silver algorithm) is a very slick way to speed up drawing the Mandelbrot set and other connected fractal sets. The idea is to calculate all the points on the boundary of a region before calculating the interior. If all the points on the boundary have the same data, then the entire interior of that regions must also have that data, and doesn't need to be calculated.

In its original form, recursive subdivision can skip small details, and it won't work at all with the process that's used to get smooth gradient coloring, since the gradient depends on knowing the trajectory of each point in the image. But it can be used to speed up drawing images that have large numbers of pixels in the interior of the set. The modified version checks only if all points on the boundary are in the interior of the set and marks all points in the interior as in-set points if they are. Since concluding that a point is in the set takes the most calculation time, this can be a big saving if many points are in the set.

News About News

I've learned a lot about how to properly manage an email newsletter over the past couple of months, and I'm making some big changes.

The biggest change is that I'm switching to a commercial email distribution service and will no longer be sending the newsletter from Outlook using BCC.

This will result in fewer weird formatting problems and a reduction in the number of times this newsletter gets flagged as junk mail. I've put together a page that goes into detail about all the reasons why the commercial distribution service is better than using Outlook. In brief:

Formatting Issues

Most webmail-type email clients totally mangle the style information in the HTML code header of emails, resulting in awful problems like black text on a black background, loss of page layout information, and other text styling information. The new email service lets me test things before sending to make sure they look right.

In addition, many people would rather receive emails in plain text. The service I'm using provides a tool to convert HTML to plain text relatively painlessly.


This newsletter has been flagged as the S word (more on why I can't say it here) quite a bit, especially by Yahoo. What I've been doing -- putting everyone's name in the BCC field of Outlook -- is actually a major red flag for S filters.

The commercial service I'm now using can send individual emails to everyone with their actual name. That looks much less like junk mail.

There are also some legal implications to this, and I'm not in the mood to get fined or put in jail. If you read the applicable Federal laws, this newsletter is in kind of a gray zone. Again, more on this here.

Tracking and Privacy

The service allows message tracking so I can monitor how frequently emails are opened, etc. I have disabled all that stuff for my account since it makes the newsletter look more like spam. Plus, even though it doesn't provide personally identifiable statistics, it still seems like spying on people.

The service is a large, well-respected service that has a strict privacy policy. Your information is safe with me and with them. I have no interest in giving anyone's email address to anyone and won't do it.


Click here for 1-click unsubscribe, no questions asked.