Stuart Hameroff on Consciousness

Beyond Belief: Science, Reason, Religion & Survival Salk Institute for Biological Studies November 5 - 7, 2006 Session 4 Stuart Hameroff, VS Ramachandran November 5, 2006 The link: http://thesciencenetwork.org/programs/beyond-belief-science-religion-reason-and-survival/session-4-1

Never Mind the Singularity, Here's the Science (Wired, 20080324)

http://www.wired.com/medtech/drugs/magazine/16-04/ff_kurzweil_sb

two single-iteration images

Introducing Z^3 and Z^4+Z^3+Z^2

Well, this first one is not really in the series of the title, but the rest below are.

The Download

Southwestern Abstract

log and floor variant of mandelbrot

Probably needs some sharpening

log variant of e^x=1

log variant of mandelbrot

This image is slightly edited. I ran "Stretch HSV" and then "sharpen".

Some b/w on a Thursday

Attn: Rockville High

Yesterday I presented itgrapher to two math classes at Rockville High School (Rockville, CT, USA). The most successful part of the presentation was when students suggested ways to alter the expressions and we watched how the images changed. To save time we did that with 200x200 images and without oversampling. Here's one of the images we did together but at higher resolution and with oversampling. Click on it to get the full resolution.

Also, one of the teachers asked about copyrights. Firstly, I'm releasing this particular image in to the public domain. In general, I reserve all rights for all my images. Here are the exceptions.

1) I don't think I can copyright (or patent) mathematical expressions. So, if you make an image using itgrapher it's yours, even if you use the equations I published for an image I originally created. You might think I'm being generous, but it works both ways. Anything I make is mine even if I use equations you publish. While you are not legally required to, I ask you politely to please credit me when you re-render my images. I also accept taxable donations (I am not a non-profit). PayPal contributions to andrewspringman (at) yahoo.com

2) Any image created with itgrapher with no further alterations that I post is licensed to all under a creative commons attribute share alike non-commercial license. In short, this means that you can make copies for yourself and your friends as long as you give me credit and don't charge anything more than the cost of materials to duplicate/print/frame etc the image.

3) I reserve all rights to any other image I post unless otherwise indicated.

Another circle variation

Pallete Knife Technique?

Prayers of the Saints

solving e ^Z = 1 with escape thresholds

Now that I have escape thresholds, calculating expressions with exp(x) becomes practical.

The complex expression exp(Z) can be rendered with the Cartesian transformation:

x <-- exp(x) * sin(y)
y <-- exp(x) * cos(y)

Yes, I looked it up in a complex math book.

It took me a while to find the right luminosity constant to render this much detail, though.

mandelbrot with high iterations and minimum threshold

I'm going to Rockville High tomorrow to talk about math and art. They expressed interest in fractals in particular, so I bit the bullet and made itgrapher practical for rendering fractals by adding an escape threshold. This is the Mandelbrot set rendered with 50 iterations and an escape threshold of 2 (which, if you read the literature, is the theoretical minimum threshold for the Mandelbrot set). Low escape thresholds make rendering fast and add these cool bubble shapes around the set. At higher thresholds, you actually get near 50 iterations without escaping for some pixels, so it takes longer. However, the bubble artifacts disappear and you get a pristine rendering.

Of course, that's why I originally added mpmath, so you didn't need to worry about how big the numbers got and you would never lose precision...but that can be very, very slow. I won't have that kind of time tomorrow.

more fun with floor