A framed dark navy print of orange and cream spiral flow lines in three swirling groups, hung on a sage wall, beside the title Phase Portrait Wall Art.
  • A framed dark navy print of orange and cream spiral flow lines in three swirling groups, hung on a sage wall, beside the title Phase Portrait Wall Art.
  • The full navy print of wavy cream and orange lines forming three oval swirls, with text on the right describing the angle and speed axes.
  • A large close-up of orange spiral lines around a cream dot on navy, next to the small print with a red square marking the crop.
  • A wide crop of the print with three dots and rings, beside a graph of a pendulum's energy falling over time, with text on damping.
  • Five navy prints in different proportions labelled 2:3, 3:4, 4:5, 11:14 and ISO A with their pixel sizes at 300 dpi.
  • The navy print in four frames of decreasing size, labelled 24 x 36 in, 16 x 20 in, 11 x 14 in and 8 x 10 in.
  • Page 1 of the Letter PDF and page 1 of the A4 PDF showing the navy print with a white margin, with notes on print settings.
  • Four boxes for the PNG zip, Letter PDF, A4 PDF and Start Here PDF, with file sizes, and a note to unzip on a computer.

Phase Portrait Wall Art

One print shows how a damped pendulum moves, as a phase portrait. Angle runs left to right and angular speed runs bottom to top, and every line follows a single motion. Each line shades from cream into orange while the pendulum loses energy. Where it hangs still, three solid dots appear and two rings sit at the unstable upside-down position. The equation is printed at the foot of the print: the angle's second derivative plus 0.22 times its first derivative plus sine of the angle equals zero. The largest file has 188 lines. The zip has 5 PNGs, one per frame ratio, and two PDFs are for a home printer.

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PNG files with a 300 dpi tag, plus Letter and A4 PDFs. A script read the PNG pixel sizes and compared the art with the equations. No test print or Acrobat check yet.

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What's included

  • Phase-Portrait-Wall-Art-PNG-5-Ratios.zip, 5 PNG files: 1 print in 5 ratios, with the license and font license text files
  • Phase-Portrait-Wall-Art-Print-at-Home-Letter.pdf, 2 pages: 1 of art, then the license
  • Phase-Portrait-Wall-Art-Print-at-Home-A4.pdf, 2 pages: 1 of art, then the license
  • Start-Here-Phase-Portrait-Wall-Art.pdf, which file fits which frame, print settings, license

How it works

  1. The full navy print of wavy cream and orange lines forming three oval swirls, with text on the right describing the angle and speed axes.
    One print, 188 lines Angle across, angular speed up. Each line follows one swing of the pendulum.
  2. A large close-up of orange spiral lines around a cream dot on navy, next to the small print with a red square marking the crop.
    Real pixels A small square cut from the 24 x 36 in file, showing one solid dot inside spiral lines.
  3. A wide crop of the print with three dots and rings, beside a graph of a pendulum's energy falling over time, with text on damping.
    What the print shows The damped pendulum equation and an energy graph. Damping only takes energy away, so each swing dies down.
  4. Five navy prints in different proportions labelled 2:3, 3:4, 4:5, 11:14 and ISO A with their pixel sizes at 300 dpi.
    Five ratios The lines were worked out again for 2:3, 3:4, 4:5, 11:14 and ISO A, so nothing is stretched.
  5. Page 1 of the Letter PDF and page 1 of the A4 PDF showing the navy print with a white margin, with notes on print settings.
    For a home printer A Letter PDF and an A4 PDF with the art 0.4 in clear of the page edge.

Compatibility and file formats

PNG files with a 300 dpi tag and indexed color, so that one zip stays under 20 MB. A script read the pixel size of each PNG and compared the art with the equations. The PDFs were drawn with poppler only. Opening the files in Adobe Acrobat Reader or Preview has not been recorded yet, and neither has a test print at home or at a print shop. The zip needs a computer or an app that can open zip files.

Instant download from Etsy · nothing shipped.

Video

Questions

Is this a real calculation?

Yes. Each line is the equation of a damped pendulum, stepped forward in time. A separate script integrated every line again with a different method and got the same path. It is a mathematical plot of the equation, not a measurement of a real pendulum.

Why do the ratios look slightly different?

The lines were worked out again for each page shape. The equation is the same, but the lines are placed afresh, so they do not fall in exactly the same spots.

Can I change the colors?

No. These are finished PNG files in navy, cream and orange.

The frames and walls in the listing images are drawn by code, and no frame or print is shipped. Colors on paper depend on your printer and paper, and no test print has been recorded. License: for your personal use only. No resale or sharing of this file. AI helped write the listing text, the how-to text and the code that builds these files. The art is computed by that code from the equations named here, and no image generator was used. Scripts tested: the pixel size and 300 dpi tag of each PNG, the size of the zip, every point of every line against a different integrator, that energy never rises along a line, and that the ink on each PNG and PDF page matches those lines. No person is claimed to have checked it unless stated here.