Translating things between languages reveals how each language approaches different design trade-offs, and I believe it’s a useful exercise. Having something to translate is the first step. I found a plot I wanted to generate, and some code that reproduced it, so off we go! I don’t recall how I originally found this page (I didn’t keep a note on it, it seems) and this has been sitting on my to-be-posted-about pile for way too long, so here’s the post I’ve been meaning to write. That post details some ALGOL code that generates Georg Nees’ “Schotter” computer-generated art from 1968 which shows a grid of squares which get increasingly displaced in position and rotation 1 'BEGIN''COMMENT'SCHOTTER., 2 'REAL'R,PIHALB,PI4T., 3 'INTEGER'I., 4 'PROCEDURE'QUAD., 5 'BEGIN' 6 'REAL'P1,Q1,PSI.,'INTEGER'S., 7 JE1.=5*1/264.,JA1.=-JE1., 8 JE2.=PI4T*(1+I/264).,JA2.=PI4T*(1-I/264)., 9 P1.=P+5+J1.,Q1.=Q+5+J1.,PS1.=J2., 10 LEER(P1+R*COS(PSI),Q1+R*SIN(PSI))., 11 'FOR'S.=1'STEP'1'UNTIL'4'DO' 12 'BEGIN'PSI.=PSI+PIHALB., 13 LINE(P1+R*COS(PSI),Q1+R*SIN(PSI))., 14 'END".,I.=I+1 15 'END'QUAD., 16 R.=5*1.4142., 17 PIHALB.=3.14159*.5.,P14T.=PIHALB*.5., 18 I.=0., 19 SERIE(10.0,10.0,22,12,QUAD) 20 'END' SCHOTTER., 1 'REAL'P,Q,P1,Q1,XM,YM,HOR,VER,JLI,JRE,JUN,JOB., 5 'INTEGER'I,M,M,T., 7 'PROCEDURE'SERIE(QUER,HOCH,XMAL,YMAL,FIGUR)., 8 'VALUE'QUER,HOCH,XMAL,YMAL., 9 'REAL'QUER,HOCH., 10 'INTEGER'XMAL,YMAL., 11 'PROCEDURE'FIGUR., 12 'BEGIN' 13 'REAL'YANF., 14 'INTEGER'COUNTX,COUNTY., 15 P.=-QUER*XMAL*.5., 16 Q.=YANF.=-HOCH*YMAL*.5., 17 'FOR'COUNTX.=1'STEP'1'UNTIL'XMAL'DO' 18 'BEGIN'Q.=YANF., 19 'FOR'COUNTY.=1'STEP'1'UNTIL'YMAL'DO' 20 'BEGIN'FIGUR.,Q.=Q+HOCH 21 'END'.,P.=P+QUER 22 'END'., 23 LEER(-148.0,-105.0).,CLOSE., 24 SONK(11)., 25 OPBEN(X,Y) 26 'END'SERIE., Schotter What’s missing from this ALGOL code is the seeds needed to reproduce the plot. The author went down a rabbit hole investigating and calculating different values, but managed to determine them to be “(1922110153) for the x- and y-shift seed, and (1769133315) for the rotation seed”. They also provided a translation into Python import math import drawsvg as draw class Random: def __init__(self, seed): self.JI = seed def next(self, JA, JE): self.JI = (self.JI * 5) % 2147483648 return self.JI / 2147483648 * (JE-JA) + JA def draw_square(g, x, y, i, r1, r2): r = 5 * 1.4142 pi = 3.14159 move_limit = 5 * i / 264 twist_limit = pi/4 * i / 264 y_center = y + 5 + r1.next(-move_limit, move_limit) x_center = x + 5 + r1.next(-move_limit, move_limit) angle = r2.next(pi/4 - twist_limit, pi/4 + twist_limit) p = draw.Path() p.M(x_center + r * math.sin(angle), y_center + r * math.cos(angle)) for step in range(4): angle += pi / 2 p.L(x_center + r * math.sin(angle), y_center + r * math.cos(angle)) g.append(p) def draw_plot(x_size, y_size, x_count, y_count, s1, s2): r1 = Random(s1) r2 = Random(s2) d = draw.Drawing(180, 280, origin='center', style="background-color:#eae6e2") g = draw.Group(stroke='#41403a', stroke_width='0.4', fill='none', stroke_linecap="round", stroke_linejoin="round") y = -y_size * y_count * 0.5 x0 = -x_size * x_count * 0.5 i = 0 for _ in range(y_count): x = x0 for _ in range(x_count): draw_square(g, x, y, i, r1, r2) x += x_size i += 1 y += y_size d.append(g) return d d = draw_plot(10.0, 10.0, 12, 22, 1922110153, 1769133315).set_render_size(w=500) print(d.as_svg()) I wanted to see if I could also translate that to R – base plot can draw line segments just fine, and I was curious about colouring the squares my own way. Most of that code translates straightforwardly, with the exception that the ‘randomness’ is actually a sequence of values, starting with a specific seed. I tooted recently about an older post of mine which (ab)uses the set.seed() function to generate specific ‘random’ words printStr

R-bloggers

A walkthrough of translating Georg Nees' 1968 'Schotter' generative art from ALGOL (via a Python implementation) into R using base plot. The key challenge is replicating a stateful pseudo-random number generator — solved in R using the <<- operator to maintain internal state inside a closure, mimicking Python's class-based approach. The post also explores variations: swapping seeds, using different seeds, and coloring squares with a viridis palette based on grid position.

Schotter Plots in R