Step

etching
1994, Amsterdam
cca 10m x 6m
in the collection of Osaka Graphic Triennale Foundation

I printed etchings for a time. A smaller clichée was printed to a huge paper many times in different structures.

Once I had the idea to construct a random structure. I wanted a chaotic pattern. soon I recognized it is not that simple as I thought. How to place randomly a cliche during printing? Humans can not directly produce a random structure. If I have a millimeter-paper and I want to put hundred random spots on it, sure, I do not spot the place in the first column on the first row. I try to simulate random, therefore I make an unwanted composition. So I covered my eyes, and I got blue spots on me, until I could recognize blindly things around the graphic workshop. Then I knew, what is where, problems started again with the unwanted composition. I blindly also followed my idea about the random. One thinks the elements should be in homogeneous distribution on the surface. Consequently try placing the new elements to where a smaller number of elements are placed. So the surface will be covered. In the reality the distribution of the randomly placed elements are only statistically homogeneous. There are huge differences between places. Only a huge number of elements produces a homogeneously covered surface. With smaller number of randomly chosen places the figure looks like composition. I decided look after these things..

Same chance

I got two dices. I divided the table of the printing machine to 36 fields. Every side had six division. I throw the two dices, one result was the row, the second is the column. The results were recorded into a figure, like the image shows below. If I got the same field again, I put a new sign in it. (On the figures the number of hits are signed with darker tones.) The placing of the elements are not continuous random, since an element is in one field, or in its neighbor, but the unwanted composition was excluded.

Inhomogenous chance

The net was small, so I made a larger one with 11x11 fields. I used two dices per sides to determine the place of the elements. I add the two dices' results together. (That's why I had to make a 11x11 grid. With two dices the smallest number can be 1+1=2, the largest 6+6=12, so from 2 to 12 there is 11 number.) I only wanted a larger random grid, but the result surprised me a much. The center of the grid was crowded with elements, and at the edges were just a few. I made two figures. The first one shows a 6x6 grid the second an 11x11 grid. The tone of the fields is rational with the number of hits.

Soon I figured out the cause of the phenomenon. A dice stays on each side with the same chance. In other words: every number has a chance 1:6. Let see, what is with the numbers from 2 to 12! For the number two, both dices has to be stay on number 1, because only 1+1 is 2. The number seven can be get from the following combinations: 1+6=7, 2+5=7, 3+4=7. It means, that number seven has three times bigger chance than number two. This can be seen clearly on the figure too. I was very proud of my discovery, while a book about number theory came into my hands. There I have seen, this discovery is one of the basic facts in number theory, known since hundred and hundred years. Then I recognized, mathematics is more, than a tool for random placing.

he small photo (right, on the top) shows a print which based on a probability wave. The print represents a three dimensional object constructed on the following way. I took a staircase from unity cubes. One step becomes higher with one unit in one unit distance. The whole object is 45 unit wide, and there are 13 steps.

A step

The axises signed with X and Y were used to determine random placings on the top of the staircase. The distribution is homogeneous by the Z axis, in fact there have every row the same chance. There are 12 sided dices, but I did not know about them. (They are used in Fantasy-games, for similar reasons.) So I had to figure out a method, how to get random numbers between 1 and 13. I used two dices. The result of the first was interesting only to be an odd or and even number. If it was an odd number, I used the result of the other dice in the interval of the X axis from 1 to 6, if it was even, I used the interval from 7 to 13.

Axonometric steps with hits

At the axis Y the method was more complex. At this axis are the probability wave. We have seen, that using two dices the small (and big) numbers has smaller chance, than the middle-numbers. Using more dices it is the same. The numbers on the middle has big chance, but the smaller ones has almost zero. (The smaller possible number using six dices is 6. To get it, all the dices must stay on number one.) The wave is too steep. And I wanted a morph from the staircase to the cubus. So I do not need a half of the wave. The first idea was to throw out the results higher, than the middle. It is a simple, but not very good idea, makes the number of necessary throws two times higher.

The half-cutting of the wave was simple. I used six dices. So I get random numbers from 6 to 36. The 6 was the same field, than 36, the 7 as 35, and so on. The other problem was solved by a seventh dice. The 45 units of the Y axis was divided into three unit divisions. I got a number one of these divisions by the six dices. Inside the division the result of the seventh dice determined the field. The first field was number 1 and 2, the second 3 and 4, and the third 5 an 6.

This method determined a place, where I put a unity cube into the staircase. If I got the same place again, I put a new cube onto the top of the previous one. This procedure was repeated many times. If a column reached the highness of the 13. step, I do not recorded anymore. I put cubes to the staircase, while the row 45 became 13 units high.

The print was made by this plan. The method of representing is axonometry, the parallel lines are parallels on the prints too. I decide this, because I want to us the same cliches to print the whole work. I used three of them, each could print a side of a unity cube.

Hit by very thin chance

The print represents the probability wave as an alternative of the 'meaning-wave'. The endpoints of the wave is the staircase and the cubus. Somewhere in the middle the two meanings neutralizes each other so much, that the space-form of the object is also not clear. The probabilities can be represented by a graph, its form is a curve. The results of the experiments are never fits exactly to this curve, because the curve is only the probability. There is no mathematical method to foresee a result of a single dice-throw. The print could be different, its final form was determined only at the two side, making one place more probably than the other. In the second row, on the fourth step there is a single cube. The chance of the throw, what determined the place was zero until four digits.

1995. január 15.