What to buy

You can buy many kinds of graphics programs.

Paint

It was invented at Apple Computer Company in 1984 by Bill Atkinson. It ran just on the Mac, was included free with the Mac and showed consumers why a Mac was better than an IBM PC: the Mac let you paint a picture on your screen, and the IBM PC couldn’t do that yet.

I explained Mac Paint in the 14^th edition of The Secret Guide to Computers. If you’d like that edition, phone me at 617-666-2666.

Mac Paint had one major limitation: it couldn’t handle colors. It handled just black-and-white, because the original Mac came with just a black-and-white screen.

(Years later, Apple began charging for Mac Paint, Ann Arbor Software invented an improved version called "Full Paint", and Silicon Beach invented a further improvement called "Super Paint". Modern Macs have color.)

It was invented in 1985 by Dan Silva in California and published by Electronic Arts. It was much fancier than Mac Paint and performed gorgeous color tricks.

It ran just on Commodore’s Amiga computer. It was why Commodore’s Amiga became popular. Because of Deluxe Paint, the Amiga quickly developed a reputation as the best computer for generating color graphics.

(Years later, the Amiga faced competition, Commodore went bankrupt, and Electronic Arts made versions of Deluxe Paint for the IBM PC and the Apple 2GS. I explain Deluxe Paint’s IBM PC version on pages 272-276.)

Windows includes a free a paint program.

Paintbrush, PC Paintbrush, and Paint are all worse than Deluxe Paint, except for Deluxe Paint’s one glaring problem: Deluxe Paint is a DOS-based program that hasn’t been updated to handle Windows and new video cards.

It runs on all popular computers (IBM, Mac, and others). While you paint, it makes funny sounds and talks to you in both English and Spanish. Besides letting you create your own shapes, it includes lots of fun little pre-drawn shapes (stars, snowflakes, trees, etc.), which you can include in your paintings to create backgrounds and pixie dust.

By using Kid Pix, you can create impressive artwork in just a few seconds! Of all the paint programs you can buy, Kid Pix is the one that give you pleasure fastest! Though the pre-drawn shapes look kid-like, they look like they come from talented kids! Kid Pix is the only program where it’s even more fun to erase your work than to create it, since Kid Pix gives you many dramatic ways to get rid of your painting, such as by dynamiting it: boom!

Educators have given Kid Pix many awards for turning kids into creative artists.

It was designed for the Mac but now also runs on the IBM PC. Painter amazes artists because it makes the computer’s screen accurately imitate different kinds of brushes, inks, and other artist tools. You can choose whether to make the screen look like you’re painting in oil, chalk, charcoal, watercolor, or whatever other medium you wish. You can fine-tune each tool, change precisely how "drippy" each tool is, and change the "bumpiness" of the paper’s texture.

It even includes a "van Gogh" mode, which lets you paint by using the same kinds of brushstrokes as the artist Vincent van Gogh.

Unfortunately, Paint is expensive ($379) and requires a powerful computer. If you have less than a Pentium (or Power Mac) with less than 16 megabytes of RAM, Paint runs too slowly to be enjoyable.

Since Paint, Dabbler, and Sketcher are intended just for creative artists who like to draw squiggles, they don’t contain commands to draw geometric shapes. For example, they don’t contain commands to draw a oval, circle, rectangle, or square. All other popular paint programs include such commands.

All paint programs suffer from the following problem:

If you use a paint program to create a shape, then try to shrink that shape, then change your mind and try to expand the shape back to its original size, the final result looks crude and lacks the details that were in the original.

That’s because a paint program shrinks a shape by using fewer pixels, and so some of the pixels that contained details are discarded. The lack of detail becomes noticeable when you try to expand the shape back to its original size.

Another problem is that when you try to rotate a shape, the shape looks cruder, because the shape’s pixels get slightly misplaced by "round-off error". If you try to rotate a shape several times, the pixels get progressively more misplaced, and the shape looks cruder and cruder.

When trying to paint, if you expand or twirl,

You get a result that makes you want to hurl.

Draw

A draw program does not store the color of each pixel. Instead, a draw program stores a memo about a geometric shape and the color of the entire shape.

For example, a draw program stores a line by storing just its starting point, angle, length, and color; it stores a circle by storing just the circle’s center, radius, and color. By contrast, a paint program would consume lots of RAM storing the color of each of the thousand of pixels that are on the line or circle.

A draw program works faster and more accurately than a paint program if you’re drawing geometric shapes. A draw program has no problem handling expansions and rotations. But it has difficulty handling squiggles, since it tries to view each squiggle as made up of many tiny arcs.

A draw program lets you name different objects, put them in front of other objects, then later move the objects to reveal objects that were hidden. Most paint programs can’t do that: in a paint program, creating a new shape automatically erases any shape that was underneath — except for a crude feature that lets you have two "layers": a "background" and a "foreground".

In a draw program, you can point to an object you drew and change its color, thickness, or style. In a paint program, the only way to change the appearance of what you drew is to draw it over again.

Unfortunately, the typical draw program is confusing to use, because when you look at what’s on your screen you’re not sure which "objects" the stuff you’re seeing is part of.

Each modern Windows word-processing program also includes a stripped-down draw program, free:

To draw while using Microsoft Word, click the Drawing button.

To draw while using Word Perfect, choose "Draw" from the Graphics menu.

To draw while using Word Pro, choose "Drawing" from the Create menu.

To draw while using Microsoft Works’ word processor, choose "Drawing" from the Insert menu.

CAD

For example, it can print mock blueprints, with the lengths of all parts marked. It can even compute the surface area (square feet) of any shape, so you can compute how much material to buy to build your structure and cover it.

It lets you give fancy geometric commands, such as "draw a 37-degree angle, but make the point be round instead of sharp, so nobody gets hurt" or "draw a circular arc that goes through these three points" or "draw a line that grazes these two circles, so it’s tangent to them".

Most CAD programs include pre-built shapes that you can put in your drawings.

Photo manipulation

Once the picture is in your computer, you can manipulate it by using a paint program. Better yet, use a program that specializes in the fine art of manipulating photographs.

Other graphics software

Deluxe Paint

In this chapter, I’ll concentrate on the IBM versions. Each IBM version requires 640K of RAM and a mouse.

Choose an IBM version

Which IBM version should you buy — Deluxe Paint 2, Deluxe Paint 2 Enhanced (which should be called Deluxe Paint 2½), or Deluxe Paint Animation (which should be called Deluxe Paint 3)?

If your computer has a poor video card (Hercules monochrome, CGA, or EGA), get Deluxe Paint 2 Enhanced.

If your computer has a good video card (MCGA, VGA, or Super VGA), get either Deluxe Paint Animation or Deluxe Paint 2 Enhanced. Deluxe Paint Animation offers animation, but Deluxe Paint 2 Enhanced offers higher resolution.

Copy to the hard disk

When you buy Deluxe Paint 2 Enhanced or Deluxe Paint Animation, you get four 5¼-inch floppies and two 3½-inch floppies.

Here’s how to copy the 5¼-inch floppies to your hard disk. (Copying the 3½-inch floppies is similar.)

Turn on the computer without any floppy in drive A. When you see the C prompt, put the PROGRAM Disk into drive A and type "a:". The computer will display an A prompt.

Type "install". The computer will say "Installation".

If you’re using Deluxe Paint Animation, press ENTER twice. If you’re using Deluxe Paint 2 Enhanced instead, press ENTER once, then type "dp" (so the screen says "dp" instead of "DPAINT"), then press ENTER again.

When the computer tells you, put the other three disks in drive A and press ENTER.

The computer will say, "Installation Complete!" (Then if you’re using Deluxe Paint 2 Enhanced, do this: type "century", press ENTER, and wait for the computer to copy fonts to the hard disk.)

Run the paint program

To start using the paint program, turn on the computer without any floppy in drive A.

To do Deluxe Paint Animation, type "do da". To do Deluxe Paint 2 Enhanced, type "do dp".

(That "do" method works if you put the DO.BAT file onto your hard disk as I recommended in the MS-DOS chapter. If you have not put DO.BAT onto your hard disk, do Deluxe Paint Animation by typing "cd da" and then "da"; do Deluxe Paint 2 Enhanced by typing "cd dp" and then "dp".)

Choose a video mode

If you’re using Deluxe Paint 2 Enhanced, you must choose a video mode. (If you’re using Deluxe Paint Animation, you don’t have to choose a video mode, and you can skip ahead to the next section.)

Deluxe Paint 2 Enhanced shows you this list of video modes:

a. CGA 320 x 200 4 colors

b. CGA 640 x 200 2 colors

c. EGA 320 x 200 16 colors

d. EGA 640 x 200 16 colors

e. EGA 640 x 350 16 colors

f. MCGA 320 x 200 256 colors

g. MCGA 640 x 480 2 colors

h. VGA 320 x 200 16 colors

i. VGA 640 x 200 16 colors

j. VGA 640 x 350 16 colors

k. VGA 640 x 480 16 colors

l. Hercules 720 x 348 2 colors

m. Tandy 320 x 200 16 colors

o. Amstrad 640 x 200 16 colors

p. Extended VGA 640 x 400 256 colors

q. Extended VGA 640 x 480 256 colors

r. Extended VGA 800 x 600 2 colors

s. Extended VGA 800 x 600 16 colors

t. Extended VGA 800 x 600 256 colors

u. Extended VGA 1024 x 768 2 colors

v. Extended VGA 1024 x 768 16 colors

Type a letter from "a" to "v". Here’s which letter to type:

Hercules monochrome "l"

CGA "a" for lots of colors, "b" for high resolution

EGA "e"

MCGA "f" for lots of colors, "g" for high resolution

VGA "f" for lots of colors, "k" for high resolution

640-by-480 512K "q" for lots of colors, "k" for high resolution

800-by-600 256K "f" for lots of colors, "s" for high resolution

800-by-600 512K "t"

1024-by-768 256K "f" for lots of colors, "u" for high resolution

1024-by-768 512K "t" for lots of colors, "v" for high resolution

If you choose a letter near the end of the alphabet ("p" through "v"), you face two complications:

The computer might say, "Specify which card is active". To reply, press the SPACE bar, look at the menu of VGA card manufacturers, and type your manufacturer’s code letter. (If your VGA card is manufactured by a company that’s not on the menu, try pretending that your VGA card is an AST VGA Plus, which handles video modes q and r.)

The computer might say, "Not enough memory". That means your computer doesn’t have enough expanded RAM. Choose a different letter instead.

Move the mouse

The mouse’s underside — its belly — has a hole in it, and a ball in the hole.

Move the mouse across your desk. As you move the mouse, remember to keep it flat and facing you. As you move the mouse, the cross moves also.

If you move the mouse to the left, the cross moves to the left. If you move the mouse to the right, the cross moves tot he right. If you move the mouse toward you, the cross moves down. If you move the mouse away from you, the cross moves up.

Practice moving the cross by moving the mouse. Remember to keep the mouse facing you at all times.

If you want to move the cross far and your desk is small, move the mouse until it reaches the desk’s edge; then lift the mouse off the desk, lay the mouse gently on the middle of the desk, and rub the mouse across the desk in the same direction as before.

Draw a squiggle

For example, try drawing a smile. To do that, put the cross where you want the smile to begin (at the smile’s upper-left corner), the depress the mouse’s left button while you draw the smile. When you finish drawing the smile, lift the mouse’s button. Then draw the rest of the face!

Click an icon

At the screen’s right edge, you see these pictures:

One-Dot Brush Squiggle

Line Arc

Filled Rectangle Filled Circle

Filled Polygon Filled Blob

Fill Spray

Brush Pickup Text

Grid Perspective

Magnify Hand

Color Pickup Symmetry

Undo Clear

Gradient Pattern

Color Indicator

Color Palette

Try this experiment: move the mouse pointer (the cross) to those icons. When the cross reaches those icons, the cross turns into an arrow.

Then put the mouse pointer in the middle of the screen, in the middle of the painting area, where you want the line to begin. Drag to where you want the line to end (by moving there while holding down the mouse’s left button).

The line you desired will appear!

Practice! Draw lines, then squiggles, then lines, then squiggles. When you feel comfortable, explore the following icons, which are more advanced.…

For example, to draw a blue object, do this: click blue, then draw the object. To erase part of an object, do this: click white, then cover the object by drawing with white paint.

If you’re using Deluxe Paint 2 Enhanced and chose a 2-color video mode, the only colors in the palette are black and white.

If you’re using Deluxe Paint Animation (or Deluxe Paint 2 Enhanced in a 256-color mode), the Color Palette icon shows just some of the colors. To see other colors, repeatedly click the Right Arrow icon (at the screen’s bottom right corner). To go back to the colors you were seeing before, click the Left Arrow icon. When you see your favorite color, click it.

Click where you want the polygon’s second corner to be. Presto — the computer draws a line from the first corner to the second corner!

Click where you want the polygon’s third corner to be. The computer draws a line from the second corner to the third corner.

Keep clicking, until you’ve clicked all the corners. Then press the SPACE bar, which makes the computer draw a line from the last corner back to the first corner and fill in the polygon.

Click in the Color Palette, at the new color you want, so it becomes the foreground color. (The new color can be red, blue, black, white, or any other color you wish.)

Click the Fill icon (which looks like a paint bucket).

The mouse pointer turns into a paint bucket. Move the mouse pointer carefully, so the tip of the paint (spilling out of the bucket) is in the middle of the large area whose color you want to change. Then click.

The entire area’s color will change to the foreground color.

If you make a mistake, click the Undo icon and try again.

You can use that technique to change the color of any big area that’s all the same color. For example, if you draw a big yellow sun, you can change the sun’s color to orange.

Here’s how to start drawing a landscape:

Clear the screen (by clicking the Clear icon). Then draw the horizon, as follows: by using the Squiggle icon, draw a horizontal black squiggle all the way across the screen. Make sure the squiggle goes all the way across the screen — from the screen’s far left to the screen’s far right — so that there are no gaps in the horizon, and so that it’s impossible to travel from the sky (above the horizon) to the ground (below the horizon) without crossing the horizon.

Then make the sky blue. To do that, click the blue part of the Color Palette icon, then click the Fill icon, then click in the middle of the sky. (If you’re using Deluxe Paint 2 Enhanced in a 2-color mode, pick black instead of blue and make a night scene.)

The entire sky will turn blue (or black).

If you made a mistake and forgot to make the horizon go all the way across the screen, the sky’s blue paint will leak through the horizon and make the ground blue. Click the Undo icon and try again!

To make the ground be desert brown or lawn green or fantasy-land purple, click your favorite ground color in the Color Palette, then click Fill, then click in the middle of the ground.

Here’s how to draw a face that’s embarrassed:

Clear the screen (by clicking the Clear icon). Begin using the Squiggle icon, draw the face’s black outline (a circle with two bumps on it — for the ears). Make sure the face’s bumpy circle is a complete circle and has no gaps. Make sure it’s impossible to go from the middle of the face to the screen’s edge without crossing the face’s circle.

Then make the face turn red. To do that, click the red part of the Color Palette icon, then click the Fill icon, then click in the middle of the face. The entire face will turn red.

If you made a mistake and forgot to make the face’s circle be complete, the face’s red paint will bleed through the gap in the face’s circle and make the rest of the screen be bloody. Yuk! Click the Undo icon and try again!

For example, try this experiment. Click the Grid icon. Draw a line (by using the Line icon). Now try to draw another line that starts at exactly the same point as the first line. Because of the grid, you don’t have to bother putting the mouse pointer exactly where the first line began; just put the mouse pointer close to that point, and the computer will automatically nudge the mouse pointer so that its coordinates are a multiple of 8 — and exactly where the first line began.

The screen splits into two parts. The left part of the screen shows the objects in their actual size; the right part of the screen shows the objects magnified.

Go ahead: continue drawing! Whatever you draw will appear in the left part of the screen (actual size) and simultaneously in the right part of the screen (magnified).

When you finish needing magnification, click the Magnify icon again. The screen will return to its usual, unmagnified state.

Click the Hand icon. (It’s also called the Grabber icon.) Put the mouse pointer in the middle of the magnified view. Drag a short distance in the direction that you want to nudge the view.

Go ahead: continue drawing! Whatever you draw will be duplicated 11 extra times, so you’ll see 12 copies of your drawing. The 12 copies are arranged in a circle and rotated, and 6 of those copies are mirror images (flipped backwards). Groovy!

When you finish symmetric drawing, click the Symmetry icon again. Then you’ll have just one mouse pointer, instead of 12.

Pop out a menu

You can make the screen display extra icons. Here’s how.

Here’s how to draw a zigzag (try it!). Drag to the Zigzag icon (which pops out of the Line icon). Then click in the painting area, where you want the zigzag to begin. Click where you want the zigzag’s first bend. Click where you want the zigzag’s second bend. Click at each additional bend. Click where you want the zigzag to end. Then press the SPACE bar. (If the zigzag’s ending point is the same as where the zigzag began, pressing the SPACE bar is optional.)

The Zigzag icon is also called the "Connected Lines" icon or "Polyline" icon.

After you’ve used the Zigzag icon, that icon stays on the screen, where the Line icon used to be.

If you ever want to draw a simple line again, make the Line icon reappear. Here’s how. Point at the Zigzag icon. Hold down the mouse’s left button. You’ll see the pop-out menu again. Drag to the pop-out menu’s Line icon.

Practice drawing zigzags, then simple lines, then zigzags again. When you feel comfortable, explore the following icons, which are more advanced.…

Click where you want the second arc to end, and click where you want that second arc to curve. Click where you want the third arc to end, and click where you want the third arc to curve. Do the other arcs.

When you finish the last arc, press the SPACE bar.

The Zigzag Arcs icon is also called the "Connected curves" icon or "Polycurve" icon.

One of them is a copy of the Squiggle icon.

To choose a different magnification level, point at the Magnify icon and hold down the mouse’s left button. You’ll see a pop-out menu that offers these magnification levels: 2x, 3x, 4x, 6x, 8x, 12x, and 16x. Drag to the magnification level you want.

Choose a brush

To draw without a computer, you can buy a collection of paintbrushes. To draw a thick line, use a thick brush. To draw a thin line, use a brush that’s tiny and fine. To create a weird texture, paint with a toothbrush. To create a big weird texture, paint with a hairbrush. To create a gigantic weird texture, get together with your friends, undress, cover yourselves with paint, and roll around on a large sheet of canvas. (That’s called Technicolor mud wrestling. It’s a quick, fun way to create an abstract pop mural. The mural makes a great conversation piece when you match the shapes on it with the various people and their parts.)

Your computer lets you paint on the screen by using all kinds of brushes. You can even invent your own brush, having any shape you like!

Here’s how to pick a brush.

Drag to whichever built-in brush interests you, and try it! The computer will use that brush to draw all shapes (squiggles, lines, arcs, etc.), until you switch to a different brush.

First, decide what shape you want the brush to produce when you tap the brush onto paper. Do you want the resulting shape to be a tiny dot, or a circle, or a square, or an irregular blob, or blob that’s the same shape as a ear, or a blob that looks like Bart Simpson’s hair, or some other weird shape?

Draw that shape in the painting area. (For example, if you want the brush’s blob to look like Bart Simpson’s hair, draw a picture of Bart Simpson’s hair.) When drawing that shape, use your favorite colors!

The computer will automatically click the Dotted Squiggle icon for you. Go have fun! Drag the mouse wherever you wish! As you drag, you’ll be drawing dotted squiggles by using your new brush and colors.

Classic computer art

During the 1960’s, many creative ideas were generated about how computers would someday create their own weird art, using a wild combination of formulas and random numbers, and unshackled by the bounds of human culture.

Here’s how to make the computer produce wild art, by using the wonderful classic tricks invented in the 1960’s and 1970’s.…

Gray levels

You can program the computer to change the gray levels in any weird way you wish, and draw the result. In the 1960’s, the Computer Technique Group of Japan did this to an ordinary photograph of John Kennedy:

Here’s what the group did to a photograph of Marilyn Monroe:

Csuri & Shaffer fed the computer a realistic line drawing of an old man; here’s what came out:

I did this with the help of a computer:

The Pin-Up has these specifications.…

scene: a scantily clad woman sitting on a stool

4 gray levels

4 symbols (1 for each gray level: a blank, a period, an asterisk, and a dollar sign)

1537 symbols altogether (53 rows × 29 columns)

In the specification, the numbers are small, yet the picture is clear. To obtain the clarity, I did non-computerized finagling.

At Bell Telephone Laboratories, Knowlton & Harmon produced a picture with much larger specifications.…

scene: two sea gulls flying in the clouds

16 gray levels

141 symbols (each gray level has several symbols; the computer chooses among them at random)

11616 symbols altogether (88 rows × 132 columns)

Instead of using blanks, periods, asterisks, and $, they used cats, battleships, swastikas, and other weird shapes. Here are the 141, listed from lightest to darkest, with some repetitions:

The picture is several feet long. Seen from a distance, it looks like this:

Here’s a close-up view of part of one of the gull’s wings:

If you don’t like sea gulls, how about Mona Lisa?

In 1971, Michael Hord made the computer turn photographs into artistic sketches. Here’s what the computer did to a photograph of his boss, and to a photograph of a colleague’s girlfriend:

To draw each sketch, the computer’s camera scanned the original photograph and found the points where the photograph changed dramatically from light to dark. Then, on a sheet of paper, it plotted those points; and through each of those points, it drew a short line perpendicular to the direction in which the original photograph darkened.

More precisely, here’s what the computer did.… It looked at four adjacent points on the original photograph:

A B

C D

It computed the darkness of each of those points. Then it computed the "darkening in the X direction", defined as:

(darkness at B) + (darkness at D) - (darkness at A) - (darkness at C)

Then it computed the "darkening in the Y direction", defined as:

(darkness at A) + (darkness at B) - (darkness at C) - (darkness at D)

Then it computed the "overall darkening", defined as:

(darkening in the X direction)² + (darkening in the Y direction)²

If the overall darkening there turned out to be large, the computer sketched a short line, in the vicinity of the points ABCD, and perpendicular to the direction of darkening. More precisely, the line’s length was 1, and the line’s slope was:

the darkening in the X direction

the darkening in the Y direction

Morphs

Here’s how to make an L slowly become a V. Notice that the letters L and V are both made by connecting three points:

Let 1" be the point halfway between 1 and 1'; let 2" be halfway between 2 and 2'; and let 3" be halfway between 3 and 3'. Then 1", 2", and 3" form a shape that’s halfway between an L and a V:

The process can be extended further:

Using that method, the Computer Technique Group of Japan gradually turned a running man into a Coke bottle, and then into Africa:

The group turned this head into a square:

Csuri & Shaffer exploded a hummingbird:

The hummingbird at the far right was obtained from the one at the far left, by moving each line a random distance and in a random direction (between 45° and -45°).

Computers can make movies. The best movie ever made by a computer is called Hunger (or La Faim). It was made under the auspices of the Canadian Film Board. It’s a 10-minute cartoon, in color, with music; but it goes far beyond anything ever done by Walt Disney. It uses the same technique as Running Cola is Africa: it shows objects turning into other objects.

It begins by showing a harried, thin executive at his desk, which has two phones. One of the phones rings. He answers it. While he’s talking on that phone, his other phone rings. To talk on both phones simultaneously, his body splits in two. (How does a single body become two bodies? By using the same technique as turning a running man into a coke bottle.)

On the other side of his desk is an armchair, which turns into a secretary, whose head turns into a clock saying 5PM, which tells the executive to go home. So he stretches his arms in front of him, and becomes his car: his hands become the headlights, his arms become the front fenders, his face becomes the windshield. You have to see it to believe it.

He drives to a restaurant and gets the waitress, who turns into an ice-cream cone. Then he eats her.

As the film progresses, he becomes increasingly fat, lustful, slothful, and miserable. In the end, he falls into hell, where he’s encircled by all the poor starving naked children of the world, who eat his flesh. then the film ends. (Don’t see it before eating dinner!)

It combines computer art and left-wing humanitarian politics, to create an unforgettable message.

Now morphing is being applied to color photographs and video images. For example, Hollywood movies use morphing to show a person gradually turning into a monster; environmentalists use morphing to show a human baby gradually turning into a spotted owl; and portrait photographers who have gone high-tech use morphing to show you gradually turning into the person you admire most (such as your movie idol or your lover).

Order versus disorder

Consider Gulls. Seen from a distance, it’s an orderly picture of gulls. Seen up close, it’s an orderly picture of a cat or battleship or swastika. But from a middling distance, it looks like disorderly wallpaper: the symbols repeat, but not in any obvious cycle. That element of disorder is what makes the picture interesting.

A first glance at Monroe in the Net shows order: a piece of graph paper. A second glance shows disorder: some of the graph’s lines are inexplicably bent. A third glance shows order: Marilyn Monroe’s face pops out at you. Her orderly face is formed from the disorder of bent lines.

Return to a Square uses arithmetic progression and geometric progression to create an over-all sense of order, but the basic elements are disorderly: a head that’s bumpy, and a panorama of weird shapes that lie uncomfortably between being heads and squares but are neither.

Many programs create disorder by random numbers. Chaos to Order uses random numbers to explode the hummingbird. Gulls uses random numbers to help choose among the 141 symbols.

An amazing example of random numbers is this picture by Julesz & Bosche:

To your eyes, the picture seems quite ordered. Actually, it’s quite disordered. One pie-shaped eighth of it is entirely random; the other seven eighths are copies of it. The copying is the only element of order, but very powerful. Try this experiment: cover seven-eighths of the picture. You’ll see that the remaining eighth is totally disordered, hence boring.

That program imitates a child’s kaleidoscope. Do you remember your childhood days, when you played with your kaleidoscope? It was a cardboard "telescope" that contained a disorganized pile of colored glass and stones, plus a series of mirrors that produced eight-way symmetry, so that what you saw resembled a giant multicolored snowflake. The program by Julesz & Bosche uses the same technique, computerized. Hundreds of programmers have imitated Julesz & Bosche, so now you can buy kaleidoscope programs for the IBM PC, Mac, Apple 2, Radio Shack TRS-80, and all other popular computers. Or try writing your own!

Take this test:

One of those is a famous painting (Composition with Lines, by Piet Mondrian, 1917). The other was done by a computer (programmed by A. Michael Noll in 1965). Which one was done by the computer? Which one do you like best?

The solution is on the next page, but don’t peek until you’ve answered!

The computer did the top one.

The programmer surveyed 100 people. Most of them (59) thought the computer did the bottom one. Most of them (72) preferred the top one — the one that was actually done by the computer.

The test shows that people can’t distinguish computer art from human art, and that the computer’s art is more pleasing that the art of a famous painter.

The computer’s version is more disordered than Mondrian’s. The computer created the disorder by using random numbers. The survey shows that most people like disorder: Mondrian’s work is too ordered. It also shows that most people mistakenly think the "computer" means "order".

Envelopes

Try this experiment. On a piece of paper, put two dots, like this:

The dots represent little insects, or "bugs". The first bug is looking at the second bug. Draw the first bug’s line of sight:

Make the first bug take a step toward the second bug:

Make the second bug run away, in any direction:

Now repeat the entire process. Again, bug 1 looks at bug 2; draw its line of sight:

Bug 1 moves toward bug 2:

Bug 2 keeps running away:

If you repeat the process many times, you get this:

The "motion of bug 1" looks like a curve. (In fact, it’s a parabola.) The "curve" is composed of many straight lines — the lines of sight. That’s how to draw a fancy curve by using straight lines.

You can program the computer to draw those straight lines. That’s how to make the computer draw a fancy curve — even if you know nothing about "equations of curves".

To get a curve that’s more interesting, try these experiments:

What if bug 2 doesn’t walk in a straight line?

What if bug 2 walks in a curve instead?

What if bug 1 goes slower than bug 2, and takes smaller steps?

What if the bugs accelerate, or slow down?

What if there are three bugs?

What if bug 1 chases bug 2, while bug 2 chases bug 3, while bug 3 chases bug 1?

What if there are many bugs?

What if they all chase each other, and their starting positions are random?

What if there are just two bugs, but the bugs are Volkswagens,

which must drive on a highway having nasty curves?

Show the bugs driving on the curved highway.

Their lines of sight are still straight;

but instead of moving along their lines of sight,

they must move along the curve that represents the highway.

What if each bug has its own highway, and all the bugs stare at each other?

Here are some elaborate examples.…

Four bugs chase each other:

The next example, called Compelling, appeared in the famous book and movie, The Dot and the Line. (Norton Juster made it by modifying art that had appeared in Scripta Mathematica.) It resembles the previous example but makes the 4 bugs start as a rectangle (instead of a square), and makes the bug in the top left corner chase the bug in the opposite corner (while looking at a nearby bug instead).

Enigmatic (from The Dot and the Line) makes 3 bugs chase each other, while a fourth bug stays motionless in the center:

I invented Kite, which makes 8 bugs chase each other:

I also invented Sails, which makes 14 bugs chase each other:

Elliptic Motion (by my student Toby D’Oench) makes 3 bugs stare at each other, while they travel on 3 elliptical highways:

Archimedean Spiral (by Norton Starr) puts bugs on circles. The bugs stare at each other but don’t move:

Fractals

Start by drawing a 1-inch line segment:

In the middle of that segment, put a bump and dip, like this:

Altogether, that bent path is 2 inches long. In other words, if the path were made of string, and you stretched the string until it was straight, the string would be 2 inches long. That’s twice as long as the 1-inch line segment we started with. So here’s the rule: putting a bump and dip in a path makes the path twice as long.

That bent path consists of seven segments. Put a bump and a dip in the middle of each segment, like this:

Altogether, those bumps and dips make the path twice as long again, so now the path is 4 inches long.

Again, put a bump and dip in the middle of each segment, so you get this:

Again the path’s length has been doubled, so now the path is 8 inches long.

If you again put a bump and dip in the middle of each segment, the path’s length doubles again, so the path becomes 16 inches long. If you repeat the procedure again, the path reaches 32 inches.

Look out your window at the horizon. What do you see? The horizon is a horizontal line with bumps (which represent hills and buildings and other objects). But on each hill, you see tiny bumps, which are trees; and on each tree, you see even tinier bumps, which are leaves; and on each leaf, you see even tinier bumps, which are the various parts of the leaf; and each part of the leaf is made of even smaller bumps (molecules), which have even smaller bumps (atoms), which have even smaller bumps (subatomic particles). Yes, the horizon is an infinitely bumpy line, a fractal!

You can buy software that creates fractals. Computer artists use fractal software to draw horizons, landscapes, and other bumpy biological objects. For example, they used fractal software to create landscapes for the Star Wars movies. You can also use fractals to draw a bumpy face that has zillions of zits.

Now you understand the computer artist’s philosophy of life: "Life’s a lot of lumps."

What’s art?

If the drawing "has potential" but isn’t totally satisfying, change a few lines of the program and see what happens — or run the program again unchanged and hope the random numbers will fall differently. The last thing to invent is the title. Whatever the drawing reminds you of becomes the title.

For example, that’s how I produced Kite and Sails. I did not say to myself, "I want to draw a kite and sails". I just let the computer pick random starting points for the bugs and watched what happened. I said to myself, "Gee whiz, those drawings remind me of a kite and sails." So I named them Kite and Sails, and pretended that I chose those shapes on purpose.

That method may seem a long way from DaVinci, but it’s how most computer art gets created. The rationale is: don’t overplan.… let the computer "do its own thing"; it will give you art that escapes from the bounds of human culture and so expands your horizons!

Modern style

Uncreative art

You’ve seen that computers can create their own weird art by using a wild combination of formulas and random numbers, unshackled by the bounds of human culture.

Today, programs such as Deluxe Paint let people use computers to create art easily and cheaply. Unfortunately, the typical person who buys a graphics program uses it to create the same kind of junk art that would be created by hand — just faster and more precisely. That’s the problem with computers: they make the production of mediocrity even easier and more glitzy.

3-D drawing

The computer drew these three-dimensional surfaces:

Those were done for the sake of art. This was done for the sake of science:

The hardest part about three-dimensional drawing is figuring out which lines the computer should not show, because they’re hidden behind other surfaces.

Coordinates

Try this experiment. Put your finger on the bridge of your nose (between your eyes). Now move your finger 2 inches to the right (so that your finger is close to your right eye). Then move your finger 3 inches up (so that your finger is near the upper right corner of your forehead). From there, move your finger 8 inches forward (so that your finger is 8 inches in front of your forehead).

You can reach any point in the universe by the same method! Start at the bridge of your nose, and get to the point by moving right (or left), then up (or down), then forward (or back).

Projecting the coordinates

To draw a picture of a three-dimensional object, put the object in front of you, and then follow these instructions.… Pick a point on the object. (If the object has corners, pick one of the corners.) Figure out that point’s X, Y, and Z coordinates (by putting your finger on the bridge of your nose and then seeing how far you must move your finger right, up, and forward to reach the object).

Then plot the point:

Go through the same procedure for every point on the object (or at least for the corners). Connect the dots and — presto! — you have a three-dimensional picture of the object! And the picture is mathematically accurate! It’s what artists call a "true perspective drawing".

To make the picture look traditionally beautiful, place the object slightly to the left of you and slightly below your eye level, so that all the X and Y coordinates become negative.

Computerizing the process

You can program the computer so that if you input a point’s X coordinate, Y coordinate, and Z coordinate, the computer will calculate the projected X coordinate (from dividing X by Z) and the projected Y coordinate (from dividing Y by Z) and plot the point on the computer’s screen (by using high-resolution graphics).

The easiest way to draw three-dimensional pictures is to buy a special three-dimensional arm that attaches to an Apple computer. To draw a picture of an object, move the mechanical arm until the arm’s finger touches the object. Immediately the arm’s software computes the X coordinate, Y coordinate, and Z coordinate of the touched point; you don’t need a ruler! It also computes the projected X coordinate and the projected Y coordinate and plots the points on your television. If you have a graphics printer, the software also plots the point on your printer’s paper.