Starship Asterisk*

Ann wrote: ↑Fri Aug 21, 2020 5:08 am
Why are parts of the image of "unwinding M51" so blurry (in the lower part of the image)? I don't think that the original Hubble image was so blurry.

• 1) the x axis is longitude
  
  2) the y axis is (basically) the
  radial distance from the South Pole

orin stepanek wrote: ↑Fri Aug 21, 2020 10:42 am Why?

Boomer12k wrote: ↑Fri Aug 21, 2020 6:20 am I am sorry, but I don't understand this... how does duplicating parts of the spiral arms, in a straight pattern... alternating the "brushes" like in a paint program to show 6-7 pointed "arms"... "unwind" a galaxy with only 2 spiral arms....yet is overlayed on a 2nd galaxy that is in reality totally disrupted and blocking the whole side of the other galaxy?

I don't understand the concept of this. Can someone please explain it? I get that it is some logarithmic spiral math function...like Fibonacci numbers...there are others in nature as well...
but this seems to be a total fantasy... and not related...

JohnD wrote: ↑Fri Aug 21, 2020 10:18 am
NGC5195 is only 2 million light years from M51, so is it really affecting the arm that happens to lie between it and us?

https://en.wikipedia.org/wiki/Archimedean_spiral wrote:

Conon of Samos

---

The Archimedean spiral (also known as the arithmetic spiral) is a spiral named after the 3rd-century BC Greek mathematician Archimedes. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line that rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation: r = a + b θ with real numbers a and b. Changing the parameter a moves the centerpoint of the spiral outward from the origin, while b controls the distance between loops. From the above equation, it can thus be stated: the position of particle from the point of start is proportional to the angle θ as time elapses. Archimedes described such a spiral in his book On Spirals. Conon of Samos was a friend of his and Pappus states that the "Archimedean" spiral was discovered by Conon of Samos.>>

BDanielMayfield wrote: ↑Fri Aug 21, 2020 1:58 pm

orin stepanek wrote: ↑Fri Aug 21, 2020 10:42 am Why?

I agree, but will hazard some guesses.

Because they could?

To make the straight parts crooked and the crooked parts straight?

Because flattening curves is the in thing now?

orin stepanek wrote: ↑Fri Aug 21, 2020 5:49 pm

BDanielMayfield wrote: ↑Fri Aug 21, 2020 1:58 pm

orin stepanek wrote: ↑Fri Aug 21, 2020 10:42 am Why?

I agree, but will hazard some guesses.

Because they could?

To make the straight parts crooked and the crooked parts straight?

Because flattening curves is the in thing now?

Thanks; I needed That!
+1

Ann wrote: ↑Fri Aug 21, 2020 5:57 pm

orin stepanek wrote: ↑Fri Aug 21, 2020 5:49 pm

BDanielMayfield wrote: ↑Fri Aug 21, 2020 1:58 pm

I agree, but will hazard some guesses.

Because they could?

To make the straight parts crooked and the crooked parts straight?

Because flattening curves is the in thing now?

Thanks; I needed That!
+1

Ann

neufer wrote: ↑Fri Aug 21, 2020 11:13 am

True-colour satellite image of Earth in equirectangular projection

---

Ann wrote: ↑Fri Aug 21, 2020 5:08 am
Why are parts of the image of "unwinding M51" so blurry (in the lower part of the image)? I don't think that the original Hubble image was so blurry.

Think of an equirectangular projection
where (for Antarctica, at least):

• 1) the x axis is longitude
  
  2) the y axis is (basically) the
  radial distance from the South Pole

Chris Peterson wrote: ↑Fri Aug 21, 2020 2:03 pm

Boomer12k wrote: ↑Fri Aug 21, 2020 6:20 am I am sorry, but I don't understand this... how does duplicating parts of the spiral arms, in a straight pattern... alternating the "brushes" like in a paint program to show 6-7 pointed "arms"... "unwind" a galaxy with only 2 spiral arms....yet is overlayed on a 2nd galaxy that is in reality totally disrupted and blocking the whole side of the other galaxy?

I don't understand the concept of this. Can someone please explain it? I get that it is some logarithmic spiral math function...like Fibonacci numbers...there are others in nature as well...
but this seems to be a total fantasy... and not related...

Agreed. I don't really get the point of this. I mean, I'm into image processing, and I love all the cool things that can be done with geometric transforms. As a technical exercise this is fun and interesting. But in terms of value in presenting information? I feel like I've lost understanding of what's going on in comparison with the original image.

BDanielMayfield wrote: ↑Fri Aug 21, 2020 8:11 pm Consensus speaks. The "whys?" have it.

I suppose at a certain level your question would be better answered by Robert Nemiroff and Jerry Bonnell. Taking a stab at it, I would say the point is education and engagement. It looks like it worked <g>. Not just this image, but the whole idea behind APOD if I may speak for Robert and Jerry.

Sure, there is nothing in the 'unwound' image that could not be measured. In fact, that has certainly been done. But like a plot that illuminates something more intuitively than a column of numbers, this image reinforces the remarkable property that spiral arms (often) obey a log spiral.

I guess I could go a bit further and say that the image demonstrates that the end of one arm closest to NGC 5195 departs from a log spiral which tends to support the idea that there has been an interaction. This too is not something that you could not deduce through analysis but the image is more accessible to a broader group.

I only glanced quickly at the discussions (semester startup and all . . . ), but here's some feedback.

- The progressive 'fuzziness' of the image as you get closer to the bottom is a consequence of the logarithmic transformation. If you look at a plot of y=ln(x), you will see it is steep at first and then flattens. Consequently, pixels that originate close to the origin (the center of M51 e.g.) get stretched more vertically due to the transformation. Additionally, the x-axis is the phase angle of the transformation. Pixels close to the origin subtend a greater angle than those far away. That stretches those pixels along the phase axis. So pixels at a small radius (near the bottom, e.g.) are quite stretched in each direction.

- NGC 5195 comes through largely unscathed for these reasons: At large r and for relatively small changes in r, y=ln(r) is approximately linear. So the y-axis maps pretty much the same way you see it. Then, the small angle approximation gives us that theta ~ sin(theta) where theta is in radians. This means that angular displacement maps to linear displacement in proportion. So the x-axis maps to what you see as well since NGC 5195 is not close to the origin.

- I think I saw a post wondering why two arms don't end up straight but opposed (?). The reason is that each arm is displaced in phase angle by roughly pi radians.

- Not sure if this was discussed, but there is no beginning or end to the image along the x (phase) axis. It just continuously repeats since you are simply wrapping around as you go. Think of it as a picture on a coffee mug that has no start or end. Hmmmmmmm <g>.

Also, who are Robert Nemiroff and Jerry Bonnell?

BDanielMayfield wrote: ↑Fri Aug 21, 2020 10:30 pm The above post was great johnnydeep, except for, GASP,

Also, who are Robert Nemiroff and Jerry Bonnell?

Look at the third line below each and every day's APOD explanation.

MoreInput wrote: ↑Sat Aug 22, 2020 7:56 am Hi all,

I did also some unwinding of different other galaxies. I posted it a year ago here: https://asterisk.apod.com/viewtopic.ph ... 73#p293173

And here is my collection of unwinded spiral galaxies and also some planetary nebulae: https://drive.google.com/drive/folders/ ... eyR4r6f9Ej

This is the galaxy M 101:

Click to view full size image

If also works for planetary nebulae, like the cat's eye nebula:

Click to view full size image

What information can we get if we look at this transformed galaxy pictures? You can follow the spiral arms more convenient and visually follow them in a straight line.

Or look at this wonderful galaxy from apod 15th May 2019:

Click to view full size image

,

Unwinded you can see the density waves ploughing through the galaxy

Click to view full size image

I fiddled the images around with GIMP using polar coordinate transformations and some other scale functions. This was done manually, so there are artifact like white lines in my images.

Best regards,
Stefan

MoreInput wrote: ↑Sat Aug 22, 2020 7:56 am Hi all,

I did also some unwinding of different other galaxies. I posted it a year ago here: https://asterisk.apod.com/viewtopic.ph ... 73#p293173

And here is my collection of unwinded spiral galaxies and also some planetary nebulae: https://drive.google.com/drive/folders/ ... eyR4r6f9Ej

This is the galaxy M 101:

Click to view full size image

If also works for planetary nebulae, like the cat's eye nebula:

Click to view full size image

What information can we get if we look at this transformed galaxy pictures? You can follow the spiral arms more convenient and visually follow them in a straight line.

Or look at this wonderful galaxy from apod 15th May 2019:

Click to view full size image

,

Unwinded you can see the density waves ploughing through the galaxy

Click to view full size image

I fiddled the images around with GIMP using polar coordinate transformations and some other scale functions. This was done manually, so there are artifact like white lines in my images.

Best regards,
Stefan

RocketRon wrote: ↑Fri Aug 21, 2020 4:25 am
Unwinding a spiral galaxy would be a bit like unscrambling an egg !

https://en.wikipedia.org/wiki/Conformal_map wrote:
<<In mathematics, a conformal map is a function that locally preserves angles, but not necessarily lengths.

• [Circles (like companion galaxy NGC 5195) map into circles]

For mappings in two dimensions, the (orientation-preserving) conformal mappings are precisely the locally invertible complex analytic functions.>>