Draw the rainbow
Piet, 838 codels, several thousand pixels
Someone had to do it:
If you save this image you can try it online!
The actual Piet program is only the top ~125 pixels, which I created using a Python program I wrote.
Editing this afterwards really hurt my vision, I'll be tripping for days!
This outputs the image in an SVG format, because SVG really is (in my opinion) the simplest way to do this. I shamelessly stole Doorknob's SVG code. Outputs:
well, this really:
<svg viewBox='0 0 400 200'><circle cx='200' cy='200' r='200' fill='red'/><circle cx='200' cy='200' r='190' fill='#ff7f00'/><circle cx='200' cy='200' r='180' fill='yellow'/><circle cx='200' cy='200' r='170' fill='lime'/><circle cx='200' cy='200' r='160' fill='blue'/><circle cx='200' cy='200' r='150' fill='indigo'/><circle cx='200' cy='200' r='140' fill='#8f00ff'/><circle cx='200' cy='200' r='130' fill='white'/></svg>
Good luck beating this answer, non-Esolang users!
MATL, 107 95 92 87 84 83 bytes
-200:200 0:200!PYyq10/k12-t8<*t0>*Q7B.561FTh.295Oh.51h4BPFTF6Bl.5hOh4B8$v255*k5M/YG
This works in current release (14.0.0) of the language/compiler.
EDIT (July 6, 2017): You can try it at MATL Online!.
To check that the colors are correct, remove the last five characters (you need to wait for a few seconds and scroll down to the end of the output).
Explanation
The code has three main steps:
Step 1: Generate a 201x401 matrix with numbers from 1 to 8. Pixels with value 1 are background (white), pixels with values 2, ..., 8 represent each band of the rainbow.
Horizontal coordinates range from -200 to 200 left to right, and vertical coordinates range from 0 to 200 bottom to top. So the origin (0,0) is bottom center, the upper left corner is (-200,200), etc.
The different bands of the rainbow are generated by computing the distance from each pixel to the origin and quantizing in steps of 10 pixels.
Step 2: Generate an 8x3 matrix defining the colormap. Each row is one of the necessary colors (white and the seven colors of the rainbow). Each value of the previous 201x401 matrix will be interpreted as an index to a row of this colormap.
We generate the colormap matrix using values between 0 and 1 for each color component, and then multiplying by 255 and rounding down. This way most values are initially 0 and 1, which will later become 0 and 255. Intermediate values are coded as values between 0 and 1 with 2 or 3 decimals, chosen so that when multiplied and rounded give the exact desired value.
Step 3: Display the image with that colormap.
% STEP 1: CREATE MATRIX DEFINING THE RAINBOW BANDS
-200:200 % row vector [-200, -199, ..., 200]
0:200 % row vector [0, 1, ..., 200]
!P % transpose and flip: convert into column vector [200; 199; ...; 0]
Yy % hypotenuse function with broadcast: distance from each point to (0,0)
q10/k % subtract 1, divide by 10, floor (round down). Gives 20 circular bands
% 10 pixels wide, with values from 0 to 19
12- % subtract 12
t8<* % values larger than 7 are set to 0
t0>* % values less than 0 are set to 0. We now have 7 bands with values
% 1, ..., 7, and the white background with value 0
Q % add 1: white becomes 1, bands become 2, ..., 8
% STEP 2: CREATE MATRIX DEFINING THE COLORMAP
7B % first row: [1 1 1] (7 converted to binary: color white)
.561FTh % second row (light purple)
.295Oh.51h % third row (dark purple)
4BP % fourth row: [0 0 1] (4 converted to binary and flipped: blue)
FTF % fifth row (green)
6B % sixth row: [1 1 0] (6 converted to binary: yellow)
l.5hOh % seventh row: orange
4B % eigth row: [1 0 0] (4 converted to binary: red)
8$v % vertically concatenate the 8 eight rows
255*k % multiply by 255 and round down. Gives exact color values
5M/ % push 255 again and divide. This is needed because colors in MATL are
% defined between 0 and 1, not between 0 and 255
% STEP 3: DISPLAY
YG % display image with that colormap
Minecraft 1.10 (almost), 2677 characters one-command, 868 blytes
Well I sure picked a verbose language.
summon FallingSand ~ ~1 ~ {Block:log,Time:1,Passengers:[{id:FallingSand,Block:redstone_block,Time:1,Passengers:[{id:FallingSand,Block:activator_rail,Time:1,Passengers:[{id:MinecartCommandBlock,Command:"summon ArmorStand ~ ~ ~ {Tags:[\"b\"]}"},{id:MinecartCommandBlock,Command:"summon Pig ~ ~ ~ {NoAI:1b}"},{id:MinecartCommandBlock,Command:setblock ~-1 ~-2 ~6 chain_command_block 3 replace {auto:1,Command:"execute @e[tag=b] ~ ~ ~ execute @e[rm=200] ~ ~ ~ tp @e[c=1] ~ -99 ~"}},{id:MinecartCommandBlock,Command:setblock ~-1 ~-2 ~5 chain_command_block 3 replace {auto:1,Command:"execute @e[tag=b] ~ ~ ~ execute @e[rm=190,r=200] ~ ~ ~ setblock ~ ~ ~ wool 14"}},{id:MinecartCommandBlock,Command:setblock ~-1 ~-2 ~4 chain_command_block 3 replace {auto:1,Command:"execute @e[tag=b] ~ ~ ~ execute @e[rm=180,r=190] ~ ~ ~ setblock ~ ~ ~ wool 1"}},{id:MinecartCommandBlock,Command:setblock ~ ~-2 ~4 chain_command_block 4 replace {auto:1,Command:"execute @e[tag=b] ~ ~ ~ execute @e[rm=170,r=180] ~ ~ ~ setblock ~ ~ ~ wool 4"}},{id:MinecartCommandBlock,Command:setblock ~ ~-2 ~5 chain_command_block 2 replace {auto:1,Command:"execute @e[tag=b] ~ ~ ~ execute @e[rm=160,r=170] ~ ~ ~ setblock ~ ~ ~ wool 13"}},{id:MinecartCommandBlock,Command:setblock ~ ~-2 ~6 chain_command_block 2 replace {auto:1,Command:"execute @e[tag=b] ~ ~ ~ execute @e[rm=150,r=160] ~ ~ ~ setblock ~ ~ ~ wool 11"}},{id:MinecartCommandBlock,Command:setblock ~ ~-2 ~7 chain_command_block 2 replace {auto:1,Command:"execute @e[tag=b] ~ ~ ~ execute @e[rm=140,r=150] ~ ~ ~ setblock ~ ~ ~ wool 10"}},{id:MinecartCommandBlock,Command:setblock ~ ~-2 ~8 chain_command_block 2 replace {auto:1,Command:"execute @e[tag=b] ~ ~ ~ execute @e[rm=130,r=140] ~ ~ ~ setblock ~ ~ ~ wool 2"}},{id:MinecartCommandBlock,Command:setblock ~1 ~-2 ~8 chain_command_block 4 replace {auto:1,Command:"tp @e[type=Cow] ~1 ~ ~"}},{id:MinecartCommandBlock,Command:setblock ~1 ~-2 ~7 chain_command_block 3 replace {auto:1,Command:"tp @e[type=Bat] ~-1 ~ ~"}},{id:MinecartCommandBlock,Command:setblock ~1 ~-2 ~6 chain_command_block 3 replace {auto:1,Command:"execute @e[type=Pig] ~ ~ ~ summon Bat ~ ~ ~ {NoAI:1b}"}},{id:MinecartCommandBlock,Command:setblock ~1 ~-2 ~5 chain_command_block 3 replace {auto:1,Command:"execute @e[type=Pig] ~ ~ ~ summon Cow ~ ~ ~ {NoAI:1b}"}},{id:MinecartCommandBlock,Command:setblock ~1 ~-2 ~4 repeating_command_block 3 replace {auto:1,Command:"tp @e[type=Pig] ~ ~1 ~"}},{id:MinecartCommandBlock,Command:setblock ~ ~ ~1 command_block 0 replace {Command:fill ~ ~-3 ~-1 ~ ~ ~ air}},{id:MinecartCommandBlock,Command:setblock ~ ~-1 ~1 redstone_block},{id:MinecartCommandBlock,Command:kill @e[type=MinecartCommandBlock,r=1]}]}]}]}
Make a new Superflat world, paste that mess into an Impulse command block, set your render distance fairly high, and run it. Break the armor stand when your computer stops lagging.
The result is 400 blocks across and 200 blocks tall, as requested.
I used MrGarretto's one command generator to pack everything together, and then modified the result of that a little bit to save a couple more bytes. Here's the input to it:
INIT:summon ArmorStand ~ ~ ~ {Tags:["b"]}
INIT:summon Pig ~ ~ ~ {NoAI:1b}
tp @e[type=Pig] ~ ~1 ~
execute @e[type=Pig] ~ ~ ~ summon Cow ~ ~ ~ {NoAI:1b}
execute @e[type=Pig] ~ ~ ~ summon Bat ~ ~ ~ {NoAI:1b}
tp @e[type=Bat] ~-1 ~ ~
tp @e[type=Cow] ~1 ~ ~
execute @e[tag=b] ~ ~ ~ execute @e[rm=130,r=140] ~ ~ ~ setblock ~ ~ ~ wool 2
execute @e[tag=b] ~ ~ ~ execute @e[rm=140,r=150] ~ ~ ~ setblock ~ ~ ~ wool 10
execute @e[tag=b] ~ ~ ~ execute @e[rm=150,r=160] ~ ~ ~ setblock ~ ~ ~ wool 11
execute @e[tag=b] ~ ~ ~ execute @e[rm=160,r=170] ~ ~ ~ setblock ~ ~ ~ wool 13
execute @e[tag=b] ~ ~ ~ execute @e[rm=170,r=180] ~ ~ ~ setblock ~ ~ ~ wool 4
execute @e[tag=b] ~ ~ ~ execute @e[rm=180,r=190] ~ ~ ~ setblock ~ ~ ~ wool 1
execute @e[tag=b] ~ ~ ~ execute @e[rm=190,r=200] ~ ~ ~ setblock ~ ~ ~ wool 14
execute @e[tag=b] ~ ~ ~ execute @e[rm=200] ~ ~ ~ tp @e[c=1] ~ -99 ~
That's a total of 15 1.9+ command blocks, and 838 bytes, so 15*2 + 838 = 868 blytes.
Here's the (almost) part, it's missing a corner and edge. It logically shouldn't - Minecraft bug? Would be exactly 400x200 blocks if it wasn't for that. Not much I can do.
