Ploughed fields via moduli

Question

Let \$R, C\$ be positive integers and let \$0 < s \leq 1\$. Consider the \$R \times C\$ matrix \$\mathbf M\$ defined as \begin{equation} M(i,j) = \frac{\mathrm{mod}\,(j, i^s)}{R^s}, \quad i = 1, \ldots, R, \quad j = 1, \ldots, C \end{equation} where \$\,\mathrm{mod}\,\$ denotes the modulo operation: for \$a,b > 0\$ not necessarily integer, \$\mathrm{mod}\,(a,b) = c\$ if and only if \$0 \leq c < b\$ and \$a = b\cdot k + c\$ with \$k\$ integer.

Note that \$0 \leq M(i,j) < 1\$.

The matrix \$\mathbf M \$ can be displayed as an image, where the value of each entry determines the color of a pixel, using a colormap to translate numbers between \$0\$ and \$1\$ into colors. The simplest colormap is to directly consider each number as grey intensity, with \$0\$ corresponding to black and \$1\$ to white.

As an example, \$R=500\$, \$C=800\$, \$s=0.8\$ with the grey colormap give the following image:

The challenge

Given two positive integers \$100 \leq R, C \leq 2000 \$ and a number \$0 < s \leq 1\$, display the above defined matrix \$\mathbf M\$ as an image. You can use any colormap of your choice, not necessarily consistent across images, as long as it satisfies the very lax requirements described next.

Colormap requirements

1. At least \$16\$ different colours.
2. Reasonably gradual changes between adjacent colours.
3. The first and last colours should be clearly different.

Although the terms reasonably gradual and clearly different are somewhat subjective, this is not likely to be a contentious point. The sole purpose of these requirements is to prevent abuse. If your programming language offers a default colormap, it is most likely fine. If it doesn't, using grey is probably the shortest option.

Additional rules

• Graphical output is required, with output being flexible as usual.
• The image should have the correct orientation, with \$M(1,1)\$ corresponding to the upper-left corner.
• The image should have the aspect ratio given by \$R\$ and \$C\$. That is, each entry of \$\mathbf M\$ should correspond to a square pixel.
• If the image is output by displaying it on the screen, it is not necessary that each screen pixel corresponds to an image pixel. That is, the display scaling is flexible (but the aspect ratio should be kept).
• Auxiliary elements such as axis labels, grid lines or a white frame are not required, but are allowed.
• Programs or functions are accepted. Standard loopholes are forbidden.
• Shortest code in bytes wins.

Test cases

Each of the following uses a different colormap, to illustrate some possibilities (and not incidentally to produce lively pictures).

Inputs: R, C, s	Output
500, 800, 0.8
600, 1000, 0.7
800, 800, 0.9
500, 900, 1
700, 1200, 0.6
200, 250, 0.3

Answer 1

Haskell, 131 bytes

f=fromIntegral
u=unwords.map show
a%b|a>b=(a-b)%b|1<2=a
(r#c)s="P2":u[c,r,99]:[u[round$f j%(f i**s)/f r**s*99|j<-[1..c]]|i<-[1..r]]

Try it online!

(r#c)s returns the lines of a PGM file.

After writing it like this, I learned I could probably just return a matrix of float values but I don't think that's very interesting.

Answer 2

J, 51 bytes

load'viewmat'
1 :'[:viewmat(|~^&u)"0~/&(1+i.)%u^~['

Try it online!

A J adverb, which uses the library function viewmat to do all the heavy lifting -- we merely need to construct the matrix values.

Assuming the adverb has been assigned to f, called like:

500 (0.8 f) 800

500 800 0.8

200 250 0.3

Answer 3

Wolfram Language (Mathematica), 39 bytes

sImage@Array[Mod[#2,#^s]&,{##}]/#^s&

Try it online!

Input [s][R, C].

Answer 4

K (oK) + iKe, 61 bytes

{w::y;h::x;p::pow[;z];,(;gray;+_255*((p 1+!h)!\:/:1+!w)%p w)}

Try it online!

Shortened heavily and made to work with the help of JohnE and coltim at the k tree.

A function which takes input as R, C, s.

Answer 5

Python 3, 116 114118 bytes

-2 thanks to some basic pointers from hyper-neutrino
+4 to correct an off-by-one error, thanks Tipping Octopus

from matplotlib.pylab import*
def M(R,C,s):
 imshow([[j%i**s/R**s for j in range(1,C+1)]for i in range(1,R+1)]);show()

Fairly straightforward, my first code golf attempt so I may be missing something easily golfable. Executes nested list comprehension inside the imshow() to immediately create image. Needs the show() to actually display the image.

700, 1200, 0.6

Answer 6

JavaScript + HTML, 156 bytes

(R,C,s)=>{for((w=x=>document.write(x))`<table cellspacing=0>`,i=0;i++<R;)for(w`<tr>`,j=0;j<C;)w(`<td bgcolor=#${((++j%i**s*16/R**s|0)*273).toString(16)}>`)}

• -7 bytes by Shaggy

; (function run() {

f=

(R,C,s)=>{for((w=x=>document.write(x))`<table cellspacing=0>`,i=0;i++<R;)for(w`<tr>`,j=0;j<C;)w(`<td bgcolor=#${((++j%i**s*16/R**s|0)*273).toString(16)}>`)}

R = /*R{*/500/*}*/;
C = /*C{*/800/*}*/;
s = /*s{*/0.8/*}*/;

document.write(`
<div style="margin-bottom: 10px;">
  <label> R = <input id="inputR" type="number" step="1" value="${R}" oninput="UpdateJS()" /></label><br />
  <label> C = <input id="inputC" type="number" step="1" value="${C}" oninput="UpdateJS()" /></label><br />
  <label> s = <input id="inputS" type="number" step="0.01" value="${s}" oninput="UpdateJS()" /></label><br />
  <form action="${location.href}" method="post">
    <input id="inputJs" type="hidden" name="js" />
    <input type="hidden" name="css" />
    <input type="hidden" name="html" />
    <input type="hidden" name="console" value="false" />
    <input type="hidden" name="babel" value="false" />
    <button type="submit">Draw</button>
  </form>
</div>
`)

f(R, C, s);

UpdateJS = function () {
  R = inputR.value;
  C = inputC.value;
  s = inputS.value;
  js = `; (${run}());`
    .replace(/\/\*R\{\*\/.*?\/\*\}\*\//, `/*R{*/${R}/*}*/`)
    .replace(/\/\*C\{\*\/.*?\/\*\}\*\//, `/*C{*/${C}/*}*/`)
    .replace(/\/\*s\{\*\/.*?\/\*\}\*\//, `/*s{*/${s}/*}*/`);
  inputJs.value = js;
};

UpdateJS();

}());

Answer 7

R, 66 bytes

function(R,C,s)cat('P2',C,R,99,(99*outer(1:C,(1:R)^s,`%%`))%/%R^s)

Try it online!

I kinda think that pajonk's answer is close to the shortest possible using R's built-in graphics... so here's a completely different approach, which actually turns-out to be 4 bytes shorter...

Outputs the contents of a greyscale PGM file. At least on my laptop using Apple's 'Preview' program, the newline characters separating lines appear to be superfluous.

Here's Preview's display of the the output of ploughed_field(500,800,.8):

Answer 8

R, 84 70 bytes

-14 bytes thanks to @Dominic

function(R,C,s)image(outer(1:C,(R:1)^s,`%%`)/R^s,c=rainbow(64),as=R/C)

Try it online!

Try it on rdrr.io with graphical output

Answer 9

Python 3, 90 73 bytes

from pylab import*;ion()
def M(R,C,s):imshow(-~r_[:C]%c_[1:R+1]**s/R**s)

Heavily based on Danica's answer, I would have commented but I have 0 reputation.

Shorter import statement

ion() to show instead of ;show()

arange (from numpy.arange) array approach for faster performance and fewer bytes

remove def function indent

   from pylab import* 
   ion()
   def M(R,C,s):imshow((arange(C)+1)%(arange(R)+1)[:,None]**s/R**s)

Thanks to ovs this shortens to 74 bytes

And a -~ trick removes 1 byte from r_[1:C+1]

Answer 10

Red, 137 bytes

func[r c s][i: make image! to[]as-pair c r k: 0
repeat y r[repeat x c[i/(k: k + 1): to 1.1.1 to[](to 1 x %(y ** s)/(r ** s)* 255)]]?(i)]	

f 500 800 0.8