CSNB Map #2

May 6, 2008

Here is another constant-scale natural boundary map of Earth called “Ocean Watersheds.”

When the edge of a world map is a natural boundary, the shape of the map has physical meaning.

World maps with natural boundaries were discovered in the mid-twentieth century by a fascinating old coot named Athelstan Spilhaus, a polymath from South Africa who, according to his obituary, spent World War II in Burma and southwest China as a meteorological sciences adviser to not-yet-chairman Mao, spent the 50’s at Area 51 sending up experimental, extremely high altitude weather balloons and about whom, because of a popular Sunday funnies science-strip Spilhaus wrote, President Kennedy said, “The only science I ever learned I learned from Athelstan Spilhaus.”

Working ingeniously with scissors and tape, Spilhaus exploited conventional projection formulas, extending them here, cropping them there, along shorelines and tectonic features to make “world maps with natural boundaries,” the title — finally, the right words together! — of his last published paper, with cartographic luminary John Parr Snyder, of 1993. The trouble, if there was one, was that he and Snyder exploited conventional projections, which, extended beyond their usual limits, became grossly distorted at their peripheries. So, even though the edges of their maps had physical meaning, it was like looking at a map of the world through a fun-house mirror. For Spilhaus and Snyder, the problem became 1) of selecting a particular projection (from hundreds available) which would minimize the fun-house effect for a given projection, and 2) of accepting the limitation of boundary extent that the chosen projection allowed. So, they could (as they did in their 1993 paper) conceive of a world map edged by continental divides, and comment on the “obvious utility” of such a map — it would organize the world into its constituent watersheds, the basic units of geomorphology — but they could not figure out how to make it.

Earth\'s Ocean Watersheds copyright 1996 Chuck Clark all rights reserved

Here is the map they would like to have made.

Because the geometry for plotting points for csnb world maps is not a conventional (two parameter, x and y) projection system — csnb only projects the line of interruption (a single parameter, x) at a constant scale — the two problems that bedeviled Spilhaus and Snyder, extreme peripheral distortion and limited boundary selection, are moot. And — here’s the bonus, the beauty of the csnb approach to making world maps — when a world map’s natural boundary is drawn at a constant scale, the map’s shape has geometrically accurate physical meaning, like looking at your reflection in a flat mirror.

Land is white, water is blue, edge of map is continental (and sub-continental) divides, and the habitual perimeters of primary ocean currents (imagine holding your finger over the end of the water hose).
What is nice here is that at a single glance you see Earth’s complete surface in proper proportion, the world’s ocean and the lands that drain into it, all in proper shape and size.

From the point of view of a raindrop, falling on the map’s edge, everything is downhill (or swept along the current). From the point of view of the sailor, coming into port, walk inland as far as you want, but beware if you go over the top of the hill. And:

  • The overall proportion of land to water is accurate
  • The relative proportion of each ocean to the others is accurate
  • The proportion (and disposition) of land draining into each ocean is accurate
  • The proportions, shape and size of the particular watersheds, relative to each other, are accurate.
  • Continents are color-coded.
  • Straits (Bering and the various Indonesian) are shown with curvy hyperlines
  • Canals (Suez and Panama) are shown with straight hyperlines (Suez, a sea level canal, has a radius corner; Panama, a locked canal, has a hard corner).

Because no segment is very large in relation to the total surface, the map folds to a pretty good globe.

If you think about the words “constant” and “scale,” it’s obvious that any csnb world map, even when its segments are very large, has to fold up, at least to some sort of volume. More about that in later posts, where I’ll cover the “children” (more compact adaptions, prunings of the boundary tree) of this map.

Gerrymandering the USA Black Belt

October 1, 2016

Found myself in a discussion yesterday about homogeneous anthropological districts, in particular the USA Black Belt.

Just thought I’d take a look at the present political representation.

This map for Euneika Rogers-Sipp

This map for Euneika Rogers-Sipp

Enceladus — for counting craters

May 11, 2016

This map corrects map-boundary imperfections in the earlier Enceladus maps.

Note the smoother curve at the both pole (left and right tips of the map), and the tangent-to-the-vertical cusp.

Enceladus centered on the north pole

Enceladus centered on the north pole

another how to . . .

April 24, 2016

. . . especially for the NASA SpaceApps VESTA REVEALED Challenge.

Here is an image from the SpringerBrief on how to prepare a segment for correct internal proportions:

Boundaries as feature edges treated as metes and bounds, transformed and reconnected using hinges and elbows

Boundaries as feature edges treated as metes and bounds, transformed and reconnected using hinges and elbows

How to . . .

April 19, 2016

If you are one of the problem solvers is the 2016 NASA Space Apps Challenge (https://2016.spaceappschallenge.org), specifically the Solar System and Beyond challenge Vesta Revealed (https://2016.spaceappschallenge.org/challenges/solar-system), this post is for you.

Here are two plates, from the monograph cited in the resources, showing what I mean by a tree, and how to convert a tree into a closed shape, a map with constant scale natural boundaries.

CSNB mapmaking using Mars' troughs (a) and ridges (b). The resulting maps will display Mar's watershed from complementary perspectives

CSNB mapmaking using Mars’ troughs (a) and ridges (b). The resulting maps will display Mar’s watershed from complementary perspectives

Making a closed shape from the trees via unzipping and hinging, as described in the NASA Apps Challenge resource. See "Mars, How the Water Runs" page (in the menu at right)

Making a closed shape from the trees via unzipping and hinging, as described in the NASA Apps Challenge resource. See “Mars, How the Water Runs” page (in the menu at right)

Enceladus “B” large file

March 16, 2016

Here’s the map in near-maximum resolution. (Click on map for full-size version)

(You might have to open it in a photo-editing software such as Photoshop. I have trouble opening this in Mac Preview.)

(Not sure if this will work; it’s the largest file I’ve yet posted.)

(Yeah. Doesn’t want to open on screen. Try right-clicking on the map and select “download linked file.”)

Suggestions welcome for how to fix this posting glitch. EDIT: the download problem appears to be native to my home computer. Enjoy the map!

Enceladus-30x63 ChuckClark2016

Enceladus gets another custom projection

January 13, 2016

Enceladus D_Titled_postI had to make up the projection. Long story. Summary is that the cut (the edge of the map) is 270˚ (three-fourths of a circle).

The purpose was to put the tiger stripes, the south polar district, into global context. Other compact maps were either unable to make the polar region large enough, relative to the nether regions, or the map periphery went squirrelly.

The cut can turn on 45˚ increments, which has the effect of rotating the stripes around the pole; the lobes refocus from leading and trailing hemispheres (the posted map) to anti- and sub-Saturnian hemispheres.

A really large version is in the works. Maybe by March, knock on wood.

Here’s what the grid looks like:

with a little Photoshopping, you could make your own! Hmm . . . would this projection be of any use on another planet or moon? Pseudo-Eisenlohr Grid

For instance, here’s the projection applied to Earth (not that you need to know where is San Luis, Argentina!). Not so useful because of the longer interruption.

Enceladus-Earth 2016

Here’s a daisy-petal foldable map of Pluto . . .

December 20, 2015

. . . in case anyone has been wanting one.

noncommercial use allowed

noncommercial use allowed

The mosaic is based on the July release, so I expect NASA will have something better for us soon.

Spaces & Illusions

October 9, 2015

My design for an children’s participatory exhibit titled Spaces & Illusions, which was  installed from 1976–1980, give or take a few months, at Atlanta’s High Museum of Art.

Its appearance here in a blog about a novel way to make world maps may appear incongruous until I offer that the process of designing and installing the exhibit presaged all the constant-scale natural boundary maps you find here.

Presaged in a cluelessly groping way, I admit, but some things take time to resolve themselves.

This image copyright Chuck Clark 2012, all rights reserved.Spaces & Illusions_ChuckClark

Enceladus Foldable Globe

January 18, 2015

Hey, if you’re visiting from papermodelers, leave a note in the comments. I’m  curious to hear what uses you put this model to! Thanks, Chuck

Enceladus_FoldableGlobe_Clark2015

Map in Progress: Earth w/Uninterrupted Oceanographics

August 1, 2014

Sure would be nice to have a simple cylindrical version of David Sandwell’s Satellite Geodesy “global” topography map, over at the Scripps Institute of Oceanography.

Say 7200×3600 pixels? Or, even better, 10,800×5400 pixels. David? David, are you out there, can you hear me?

Below I had to cobble in the poles from another source, so both the color match and data match are off.

Map in progress, with currents from multiple sources, Creative Commons copyright Chuck Clark 2014:

CSNB_M_ChuckClark_2014