Skip to main content
Scientific American
  • Cart 0
  • Forgot password?Loading
    Not yet registered?
  • |Newsletters
Advanced Search
  • Coronavirus
  • Health
  • Mind & Brain
  • Environment
  • Technology
  • Space & Physics
  • Video
  • Podcasts
  • Opinion
  • Store
  • Subscribe
  • Current Issue
  • Cart0
  • Sign In
  • Newsletters
      • Share
      • Latest

      Polynomial Plot: Simple Math Expressions Yield Intricate Visual Patterns [Slide Show]

      Plotting the roots of run-of-the-mill polynomials yields dazzling results

      • Share on Facebook
      • Share on Twitter
      • Share on Reddit
      • Share on LinkedIn
      • Share via Email
      • Print
      Polynomial Plot: Simple Math Expressions Yield Intricate Visual Patterns [Slide Show]
      Slideshow (7) images
      View
      Credits: SAM DERBYSHIRE

      Polynomial Plot: Simple Math Expressions Yield Intricate Visual Patterns [Slide Show]

        • Share
      • 7 This crop shows the detail of an inner edge of the main ring in Derbyshire's image. It is a favorite of John Baez, a mathematical physicist at the University of California, Riverside, who posted these images on his Web site... SAM DERBYSHIRE
      • 6 Around the number 4/5, a white line again traces the real axis—Derbyshire's polynomials have a seemingly continuous collection of real roots in the vicinity. But above and below the axis, the imaginary numbers form intricate flame-like patterns... SAM DERBYSHIRE
      • 5 This crop of Derbyshire's image shows intriguing patterns around the imaginary number i, the square root of –1. SAM DERBYSHIRE
      • 4 Derbyshire's image of 24th-degree polynomial roots with coefficients of either 1 or –1 features a serrated hole around the root 1. The white line slicing through the image traces the horizontal (or real) axis—the line comprises the real roots of the polynomials... SAM DERBYSHIRE
      • Advertisement
      • 3 Sam Derbyshire, an undergraduate student at the University of Warwick in England, took a large but very specific set of polynomials to make this rich plot, comprising hundreds of millions of individual roots... SAM DERBYSHIRE
      • 2 This crop of the previous slide reveals details of the hole near i on the vertical (imaginary) axis, which appears at the top center of the image and in greater detail in the inset. (The different colors of the points represent roots of polynomials of different degrees.) Note that i appears as a polynomial root but its closest neighbors do not... DAN CHRISTENSEN, UNIVERSITY OF WESTERN ONTARIO
      • 1 Dan Christensen, a mathematician at the University of Western Ontario, plotted the roots of polynomials of degree six or less whose coefficients are integers between –4 and 4. The collection has large holes surrounding the points 0, 1 and –1 on the real axis—although some polynomials have those numbers as roots, the numbers nearby (especially those incorporating an imaginary component) seem to be off-limits... DAN CHRISTENSEN, UNIVERSITY OF WESTERN ONTARIO
      • Previous
      • Next
      of
      • View all
      • Link copied!
      • 7
      • 6
      • 5
      • 4
      • 3
      • 2
      • 1
      Advertisement
      Advertisement

      Newsletter

      Get smart. Sign up for our email newsletter.

      Sign Up

      Support Science Journalism

      Discover world-changing science. Explore our digital archive back to 1845, including articles by more than 150 Nobel Prize winners.

      Subscribe Now!Support Science Journalism

      Follow us

      • instagram
      • soundcloud
      • youtube
      • twitter
      • facebook
      • rss

      Scientific american arabic

      العربية
      • Return & Refund Policy
      • About
      • Press Room
      • FAQs
      • Contact Us
      • Site Map
      • Advertise
      • SA Custom Media
      • Terms of Use
      • Privacy Policy
      • California Consumer Privacy Statement
      • Use of cookies/Do not sell my data
      • International Editions
      Scientific American is part of Springer Nature, which owns or has commercial relations with thousands of scientific publications (many of them can be found at www.springernature.com/us). Scientific American maintains a strict policy of editorial independence in reporting developments in science to our readers.

      © 2022 Scientific American, a Division of Springer Nature America, Inc.

      All Rights Reserved.

      Scroll To Top

      Support science journalism.

      Scientific American paper issue and on tablet

      Thanks for reading Scientific American. Knowledge awaits.

      Already a subscriber? Sign in.

      Thanks for reading Scientific American. Create your free account or Sign in to continue.

      Create Account

      See Subscription Options

      Continue reading with a Scientific American subscription.

      You may cancel at any time.

      Sign in.