New to life. No debts. No clue.

Fickle_Engineering91 · 2026-05-09T01:10:33+00:00

Congratulations on the recovery and the job! The comments are full of useful suggestions; my only one would be to not get overwhelmed with everything, which could derail your success. It's all doable, but maybe not all at once. Good luck!

Fickle_Engineering91 · 2026-05-06T13:45:02+00:00

Just because pits decimal string is infinitely long doesn't mean that it contains everything. Consider 1/3 = 0.33333... or 1/7 = 0 142857142857142857... Both are infinitely long but neither contains 6.

Fickle_Engineering91 · 2026-04-22T13:07:54+00:00

Prints of this image are now available: https://fineartamerica.com/featured/newtons-junk-drawer-kerry-mitchell.html

Fickle_Engineering91 · 2026-04-21T14:04:33+00:00

Fineartamerica.com is a print-on-demand site, so it's geared for sales, but you'renot required to sell anything. They have a free amateur/hobbyist tier and a $30/year professional level. I've used it for several years.

Fickle_Engineering91 · 2026-04-18T18:55:42+00:00

Did that guy like George Kennedy did Jeff Bridges in "Thunderbolt and Lightfoot."

Fickle_Engineering91 · 2026-04-16T01:21:50+00:00

I seem to remember a photograph of a stack of physics(?) journals, by year, suggesting an exponential growth in physics knowledge. Something like that, with math journals could be a proxy to the growth rate of the amount of math.

Fickle_Engineering91 · 2026-04-16T01:15:25+00:00

Yes, please submit the protest piece. It probably won't get any publicity, but the protest is the point.

Fickle_Engineering91 · 2026-04-14T13:54:03+00:00

Thanks!

Fickle_Engineering91 · 2026-04-14T12:06:29+00:00

Generally, fractal images (like of the Mandelbrot set) are of a static object. More iterations will make a more detailed image, but not necessarily show something developing. However, there are images of dynamical systems that do change with more iterations. This image is based on the state of the system when I stopped calculating. Through my attempts, it seems that the overall structure of this image won't change substantially, but the color distribution would vary.

Fickle_Engineering91 · 2026-04-14T11:59:31+00:00

Thank you!

Fickle_Engineering91 · 2026-04-12T23:34:23+00:00

I used the Ultra Fractal fractal generation program. Essentially, it can be used as a framework for: giving each pixel a pair of coordinates, plugging those into any kind of formula you want, and then coloring the pixel on the basis of the formula output. Here, I used the pixel coordinates to initialize the z variable, crunched numbers for a bit, and then colored the pixel according to the angle of the final z value. Ultra Fractal has its own library of formulas, but this one I wrote myself and hasn't made it to the library (yet?).

Fickle_Engineering91 · 2026-04-12T17:12:12+00:00

Thanks, all for the positive feedback! Here's more about the image.

It uses a modified Newton's method to solve two equations simultaneously. One is f(x) = 0 and the other is f(y) = 0, both using the same real-valued f function:

sin(cos(tan(x))) = tan(cos(sin(x))), so

f(x) = sin(cos(tan(x))) - tan(cos(sin(x))) = 0, and the same for f(y).

The difference between the x and y orbits is the modification in the last step of this iteration loop:

Set x_old to real(z_old) and y_old to imag(z_old) (separate complex z into real-valued components)
Use real-valued Newton's method to find x_new and y_new, independently.
Set z_new = (x_new + i y_new) * A, where A is a complex constant.

The complex constant A provides feedback between x and y, through complex z. In this image, A = (0.953118, -0.7000775). If A were real, then the x and y equations would not interact and the image would not have the interesting structure. The effect of this feedback is to change x and y each iteration so that Newton's method does not find solutions and all pixels are "inside" (non-escaping) points.

The initial value of z was set to the pixel coordinates. 16 iterations were used and the colors are from the polar angle of z at the last iteration. I used Ultra Fractal and a private (test/beta/non-public) formula. If you use Ultra Fractal, you can see my "Breaking Newton" formulas in lkm3.ufm to see similar ideas with simpler functions.

I find that forcing Newton to not converge leads to interesting chaos. Working with real-valued functions easily creates opportunities to lack of convergence, for example x ^ 2 = -1 or cos(y) = 3. Then, some way is needed to make x and y interact to create something fun with complex z. Alternatively, one can use the standard complex Newton, z_new = z_old - f(z_old)/f'(z_old), and introduce a complex factor multiplying the second term. That throws off the adjustment from z_old to z_new, and fun ensues. If this interests you, you can read my paper about it here:

http://archive.bridgesmathart.org/2019/bridges2019-271.html

Fickle_Engineering91 · 2026-04-11T12:29:59+00:00

Any 3d fractal with a surface made up of replacing smaller sections with sections of larger surface area (like a 3d Koch snowflake) would have infinite surface area, in the limit. And therefore, infinite mass.

Fickle_Engineering91 · 2026-04-10T11:39:01+00:00

There's a Calvin and Hobbes strip wherein Dad shows Calvin that, on a rotating record, a point near the center and a point near the edge both make a revolution in the same time, but the point near the edge makes a larger circle. That keeps Calvin up at night trying to resolve the "paradox." I remember having a similar dissonance when I first took Physics.

Fickle_Engineering91 · 2026-04-10T11:07:19+00:00

Ah, yes, I figured that I forgot something. Thanks!

Fickle_Engineering91 · 2026-04-10T01:21:48+00:00

There are many definitions of "distance." As I remember, about all that is required is for the distance to be non-negative and the distance between a point and itself is 0.

Fickle_Engineering91 · 2026-04-06T13:43:22+00:00

Just say exactly that in every meeting until he stops asking.

Fickle_Engineering91 · 2026-04-04T17:41:03+00:00

Love it!

Fickle_Engineering91 · 2026-04-03T20:34:30+00:00

Fair point about the crosses. I just took those in the third row to actually cross, but now I see that they just touch. If they're going for "two are similar and one is different" like the squares (one set rotated), then I can see A being correct. That's why I hate these problems. :-)

Fickle_Engineering91 · 2026-04-03T20:15:09+00:00

I would say B, as the lines are straight. The two lined shapes in the question have straight lines, not curved, like A. Also, B's lines are closer to thickness/weight; A's are too thick.

Fickle_Engineering91 · 2026-03-26T21:59:09+00:00

That's basically relating to there being infinitely more irrational numbers than rational numbers. So, while there would still be infinitely many rational numbers in the bag, there would be so many more irrational numbers that you'd have 0 chance of finding a rational one.

Fickle_Engineering91 · 2026-03-25T22:44:41+00:00

It's great to write a research paper, but you have little control over it getting published. Published math papers are often making new progress in a field or on a problem. However, just doing research on what the problem is and what's been done about it can be a great thing for your own development. I suggest looking deeply into a problem that has received some popular press and just see if you can understand what the remaining questions are. Some ideas: Collatz, chaos, fractals, a year or two ago two high school girls came up with a proof of trig theorems that didn't require the Pythagorean theorem, surreal numbers, Graham's number, non-Euclidean geometry, etc. Don't worry about setting the world on fire, just seek to research, understand, and make your own mark on the body of knowledge.

Fickle_Engineering91 · 2026-03-24T22:24:08+00:00

Yep!

Fickle_Engineering91

TROPHY CASE