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Desmond Paul Henry

Desmond Paul Henry $(1921-2004)$ was a Manchester University Lecturer and Reader in Philosophy. He was one of the British pioneers of Computer Art.

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Henry with Drawing Machine 2, 1964

During the 1960's he constructed three drawing machines based around the components of a Norden analogue bombsight computer. These computers were employed in World War II bomber aircraft to calculate the accurate release of bombs.

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Norden bombsight computer

Henry's electronically operated machines relied mainly on the "mechanics of chance". This meant they could not be programmed or store information as in a conventional computer, nor were they precision instruments. As a result, Henry had only overall control, but he could spontaneously intervene to direct the course of image production.

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Henry's Drawing Machine 1

Henry's machine drawings were forgotten until their reappearance in the $2010$ “Digital Pioneers” exhibition at the Victoria & Albert Museum in London.

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Image produced by Drawing Machine $1$ $(1962)$

Similarities

Henry’s machines produced abstract, curvilinear, repetitive line drawings. He compared his images to those produced with harmonographs and ornamental geometric lathes.

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Max Ernst making Lissajous figures with his harmonograph, New York, $1942$

Since $1950$ Benjamin Francis Laposky photographed the screen of a modified oscillograph combined, among others, with a sinus wave generator.

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Benjamin Francis Laposky, Oscillon Number Four, $1950$

My attempt

A modified Poincaré Map was the closest I got to Henry's winding and swirling random patterns:

data =
  Reap[
   NDSolve[{
     x''[t] + 0.2 x'[t] - x[t] + x[t]^3 == 0.3 Cos[t],
     x[0] == 0,
     x'[0] == 0,
     WhenEvent[Mod[t, Pi/2] == 0,
      Sow[{
        x[t],
        x'[t]}]]},
    {},
    {t, 0, 200000}]];

Unfortunately, it produces points, not lines:

ListPlot[data[[2]],
 AspectRatio -> 0.7,
 Axes -> False,
 Background -> Black,
 PlotStyle -> Directive[GrayLevel[0.5], PointSize[.002]]]

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My attempt

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Desmond Paul Henry

My request

I want to reproduce one of Henry's spiralling line patterns with Mathematica (similar to the one below; the coloring is optional). More of them can be seen here: desmond henry gallery

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    $\begingroup$ I have to admit that I am so much used to high-quality presentations by you in this topic, that I first clicked the upvote, then left a comment and now I am going to enjoy some art-maths-coding information. $\endgroup$
    – bmf
    Commented Mar 1 at 9:13
  • 3
    $\begingroup$ I agree with @bmf . I would happily purchase a compendium of what you’ve written—and what you’ve learned from the community. $\endgroup$ Commented Mar 1 at 12:57

1 Answer 1

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An attempt:

SeedRandom[5];
random = RandomReal[2, {10, 2}] & /@ Range[10];
ptsA = Table[
   Map[Dot[RotationMatrix[-1/10 \[Theta]  ] , #] &, 
    Table[Cos[#1] + i    Sin[(#2 - #1)], {i, 0, 1, .1}] & @@ 
     random, {2}], {\[Theta] , Pi/4, 4 Pi, Pi/3}];


SeedRandom[2];
random = RandomReal[1.5, {10, 2}] & /@ Range[10];
ptsB = Table[
   Map[Dot[RotationMatrix[1.3  Pi - 1/8 \[Theta]  ] , #] &, 
    Table[Cos[#1] + i    Sin[(#2 - #1)], {i, 0, 1, .1}] & @@ 
     random, {2}], {\[Theta] , Pi/2, 8 Pi, Pi/3}];


SeedRandom[1];
random = RandomReal[2, {10, 2}] & /@ Range[10];
ptsC = Table[
   Map[Dot[RotationMatrix[1/20 \[Theta]  ] , #] &, 
    Table[Cos[#1] + i    Sin[(#2 - #1)], {i, 0, 1, .1}] & @@ 
     random, {2}], {\[Theta] , 0, 2^3 Pi, Pi/2}];

Show[
   Map[Graphics[ {Opacity[.3], RGBColor[.7, .3, .3], BSplineCurve[#, SplineClosed -> True, SplineDegree -> 5]} ] &, ptsA]
 , Map[Graphics[ {Opacity[.3], RGBColor[.6, .4, .4], BSplineCurve[#, SplineClosed -> True, SplineDegree -> 5]} ] &, ptsB]
 , Map[Graphics[ {GrayLevel[0, .1],  BSplineCurve[#, SplineClosed -> True, SplineDegree -> 5]} ] &, ptsC]
 , ImageSize -> Large]

enter image description here

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    $\begingroup$ Thank you, vindobona, that's very beautiful and a true replica $\endgroup$
    – eldo
    Commented Mar 2 at 16:04
  • $\begingroup$ @eldo Glad you enjoyed it :-). Thank you for all these exceptional art related posts. $\endgroup$
    – vindobona
    Commented Mar 2 at 16:50
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    $\begingroup$ How did you do this just by looking at the pic, I am very impressed. $\endgroup$ Commented Mar 5 at 18:55
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    $\begingroup$ @EduardoSerna Thank you! Regarding how I did it :-) ... I started with the basic formula for the points of the BSplineCurve and afterwards by using Manipulate and different seeds I went through several combinations in order to get somehow closer to the spiralling line patterns seen in the picture. $\endgroup$
    – vindobona
    Commented Mar 7 at 19:05

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