From 3036e055435d18c46a7ca205bdaf54e4948ee850 Mon Sep 17 00:00:00 2001 From: juergen Date: Sun, 28 Sep 2025 18:45:36 +0200 Subject: [PATCH] Add analog Lorenz attractor project documentation --- about.md | 4 +- .../LorenzAttractor_720p30_diverge_2.mp4 | Bin 0 -> 4004123 bytes .../analog-lorenz/analog-lorenz_bottom.jpg | Bin 0 -> 116767 bytes .../analog-lorenz/analog-lorenz_display.jpg | Bin 0 -> 53557 bytes .../analog-lorenz/analog-lorenz_top-back.jpg | Bin 0 -> 106993 bytes .../analog-lorenz/analog-lorenz_top-front.jpg | Bin 0 -> 113965 bytes projects/analog-lorenz/analog-lorenz.md | 130 ++++++++++++++++++ projects/projects.md | 11 ++ 8 files changed, 144 insertions(+), 1 deletion(-) create mode 100644 media/projects/analog-lorenz/LorenzAttractor_720p30_diverge_2.mp4 create mode 100644 media/projects/analog-lorenz/analog-lorenz_bottom.jpg create mode 100644 media/projects/analog-lorenz/analog-lorenz_display.jpg create mode 100644 media/projects/analog-lorenz/analog-lorenz_top-back.jpg create mode 100644 media/projects/analog-lorenz/analog-lorenz_top-front.jpg create mode 100644 projects/analog-lorenz/analog-lorenz.md create mode 100644 projects/projects.md diff --git a/about.md b/about.md index 16eb065..af70c07 100644 --- a/about.md +++ b/about.md @@ -17,7 +17,9 @@ Dadurch sind schon einige Projekte entstanden: * Die LED Decke, die nicht nur die Lounge beleuchtet, sondern auch als Bildschirm funktioniert * Das DocPatch, das alle Änderungen an unserem Grundgesetz als Open-Data Projekt visualisiert -Viele weitere Projekte findest du [in unserem Wiki](https://wiki.chaospott.de/projekte:start). +Weitere Informationen zu unseren Projekten findest du +[hier]({{ site.url }}/projects/projects.html) und +[in unserem Wiki](https://wiki.chaospott.de/projekte:start). --- diff --git a/media/projects/analog-lorenz/LorenzAttractor_720p30_diverge_2.mp4 b/media/projects/analog-lorenz/LorenzAttractor_720p30_diverge_2.mp4 new file mode 100644 index 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+ +

+Im Video startet das Lorenz-System mit zwei Zuständen, +die nur einen Abstand von 1/1000 in Z-Richtung haben. +Dort wo sie übereinander liegen, verdeckt die grüne Linie die blaue. +Das Video wurde mit [Manim](https://www.manim.community/) erzeugt, +mit [diesem Quellcode](https://git.chaospott.de/starblue/manim-lorenz). + +[^2dim]: Tatsächlich gibt es noch winzige Abweichungen von der Fläche, + je nachdem in welcher Folge der Zustand vorher rechts- oder linksherum + gelaufen ist. + Deshalb hat der Attraktor eine etwas höhere fraktale Dimension + (ca 2,05), je nach Parametern und verwendeter Definition von Dimension. + +## Die Schaltung + +![Vorderansicht der Schaltung]({{site.url}}/media/projects/analog-lorenz/analog-lorenz_top-front.jpg) + +Die Schaltung wurde frei nach [dieser Schaltung](http://seti.harvard.edu/unusual_stuff/misc/lorenz.htm) +von Paul Horowitz gebaut. +Es ist ein Analogrechner, der die Bahn des Lorenz-Systems in Form +von drei Spannungen berechnet. + +Dabei werden die reinen Zahlen in physikalische Größen übersetzt: + +- x, y und z entspricht den Ausgangsspannungen der Operationsverstärker in Volt, + wobei der Ausgang für y negiert ist. +- Die Parameter im Lorenz-System werden durch Widerstände realisiert. + Wenn man jeweils den Kehrwert des Widerstands, d.h. den Leitwert, betrachtet, + entspricht 1 einem Mikro-Siemens (1µS = 1/1MΩ). + - 100kΩ entspricht 10µS für den Parameter s. + - 35,7kΩ entspricht 28µS für r. + - 374kΩ entspricht 2.68μS ~ 8/3μS für b. +- Am negativen Eingang der Operationsverstärker werden + die durch die Widerstände skalierten Ströme addiert + und die Summe dann im Kondensator integriert. + +Aus Verfügbarkeitsgründen haben wir einige Bauteile durch andere ersetzt, +die aber die gleiche Funktion haben: +- Für die Analog-Multiplizierer verwenden wir zwei AD633N im DIP-8 Gehäuse, +- für die Operationsverstärker einen 4-fach OpAmp TL084 im DIP-14 Gehäuse, und +- für die krummen Widerstandswerte 35,7kΩ und 374kΩ Reihenschaltungen + von jeweils einem Festwiderstand und einem Potentiometer. + +Bei den Kondensatoren sind jeweils vier Werte 100pF, 1nF, 10nF und +100nF verbaut, die mit einem Drehschalter mit 3 Polen und 4 Stellungen +parallel umgeschaltet werden können. Dadurch kann die Geschwindigkeit +pro Schritt um einen Faktor von 10 geändert werden, und insgesamt +liegt dadurch ein Faktor von 1000 zwischen der langsamsten und der +schnellsten Einstellung[^caps]. + +[^caps]: Die schnellste Einstellung ist etwas zu schnell, es entstehen Artefakte. + Außerdem ist die Abstufung mit dem Faktor 10 sehr grob, + besser wäre vielleicht 1nF, 3,3nF, 10nF, 33nF. + +Zusätzlich gibt es ein Potentiometer, mit dem man eine Konstante zum x-Wert +hinzuaddieren kann. Damit kann man den Attraktor etwas zu einer Seite verschieben, +bei zu großen Werten kollabiert er aber dann in einen Punkt ("Klimawandel"). + +Die Betriebsspannung ist 30V. +Intern wird das als ±15V betrachtet, mit einer virtuellen Masse für 0V. +Der eigentliche analoge Arbeitsbereich ist ±10V. + +In der Schaltungen sind die Drähte für x rot, für y grün und für z blau[^colors]. +Der vierte Operationsverstärker wird für die virtuelle Masse verwendet, +das ist der mittige Draht zwischen den ICs auf der Unterseite. + +[^colors]: Aber nicht alle roten Drähte sind für x und nicht alle blauen für z. + Rot und blau werden auch für die positive und negative + Versorgungsspannung verwendet. + +![Rückansicht der Schaltung]({{site.url}}/media/projects/analog-lorenz/analog-lorenz_top-back.jpg) + +Als Anzeige verwenden wir ein Tektronix 2213 Analog-Oszilloskop im XY-Modus. +Am X-Eingang (Kanal 1) des Oszilloskops wird der x-Wert des Lorenz-Systems angeschlossen, +am Y-Eingang (Kanal 2) der z-Wert. +Dadurch ergibt sich dann die einem Schmetterling ähnliche Form des Attraktors. + +Kanal 1 (x) steht auf 0,5V pro Teilung, Kanal 2 (z) auf 1V pro Teilung +(für 1x Probe). +Weil die z-Werte positiv sind, muss die vertikale Position entsprechend +angepasst werden. + +![Ansicht der Schaltung von der Lötseite]({{site.url}}/media/projects/analog-lorenz/analog-lorenz_bottom.jpg) diff --git a/projects/projects.md b/projects/projects.md new file mode 100644 index 0000000..d777436 --- /dev/null +++ b/projects/projects.md @@ -0,0 +1,11 @@ +--- +layout: post +title: Projekte +--- + +Hier dokumentieren wir einige unserer Projekte ausführlicher. +Weitere Projekte finden sich [in unserem Wiki](https://wiki.chaospott.de/projekte:start). + +## [Der analoge Lorenz-Attraktor](analog-lorenz/analog-lorenz.html) + +Eine Analogschaltung, die den Lorenz-Attraktor auf einem Analog-Oszilloskop darstellen kann.

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