This example is the final version for the “Sierpinski Challenge”, an exciting challenge regarding fractals. This example reproduces the famous “SIERPINSKI TRIANGLE” on retrocomputers. It is a very simple fractal to obtain, which takes its name from the mathematician who first studied its properties. Such a triangle can have different shapes and sizes and can be obtained in various ways. One of the methods to create it is the so-called “Game of chaos”. The fractal is built by creating iteratively a sequence of points, starting from a random initial point, in which each point of the sequence is a given fraction of the distance between the previous point and one of the vertices of the polygon; the vertex is chosen at random in each iteration. Repeating this iterative process a large number of times, selecting the vertex at random at each iteration, often (but not always) produces a fractal shape. Using a regular triangle and the factor 1/2, it will result in a Sierpinski triangle.

 
 ' ============================================================================
 ' INITIALIZATION / INIZIALIZZAZIONE
 ' ============================================================================
 
 ' Let's start measuring the execution time from the first useful instruction. 
 ' Then we also measure the time it takes to initialize the graphics subsystem 
 ' and clear the screen.
 ' 
 ' Iniziamo la misurazione del tempo di esecuzione dalla prima istruzione utile. 
 ' Quindi misuriamo anche il tempo che impiega a inizializzare il sottosistema 
 ' grafico e a cancellare lo schermo.
 '
 t=TI
 
 ' With this command we ask ugBASIC to select a "bitmap" mode (ie where it is 
 ' possible to draw "pixel by pixel") resolution of preference. In the specific 
 ' case, a resolution of 320 pixels wide by 200 pixels height, for a maximum 
 ' of two colors per pixel, is requested. This request must be understood as a 
 ' suggestion: it is possible that the hardware on which the program will run 
 ' may not have this resolution, or perhaps the minimum number of colors 
 ' is 16. It will be the programmer's responsibility to adapt the program so 
 ' that it can work in every situation.
 '
 ' Con questo comando chiediamo a ugBASIC di selezionare una modalità "a bitmap" 
 ' (cioè dove sia possibile disegnare "pixel per pixel"), con una risoluzione di 
 ' preferenza. Nel caso specifico, una risoluzione di 320 pixel di larghezza 
 ' per 200 pixel di altezza, per un massimo di due colori per pixel. Questa 
 ' richiesta deve essere intesa come un suggerimento: è possibile che l'hardware 
 ' su cui girerà il programma non possa disporre di questa risoluzione, o 
 ' magari il numero di colori minimo è 16. Sarà responsabilità del programmatore
 ' adattare il programma affinché possa funzionare in ogni situazione.
 '
 BITMAP ENABLE(320,200,2)
 
 ' Let's set the black color for the pixels to be drawn.
 '
 ' Impostiamo il colore nero per i pixel da disegnare.
 '
 INK BLACK
 
 ' Let's clear the screen, setting the background color as white.
 '
 ' Cancelliamo lo schermo, impostando il colore di sfondo come bianco.
 '
 CLS WHITE
 
 ' Now let's calculate the size of the window (screenWidth x screenHeight pixels) 
 ' within which we will draw the Sierpinski triangle. As a general rule, we will
 ' use a window of 256 pixels wide by a height equal to the maximum that can be 
 ' represented by the hardware. If there are fewer than 256 pixels available, 
 ' we'll use those. If there are more than 256 pixels available, the triangle 
 ' will be centered on the screen (by using and offset of offsetX pixels).
 '
 '           |----------- screenWidth -----------|
 ' +-------------------------------------------------------+
 ' |<------->+-----------------------------------+<------->|---
 ' | offsetX |                                   | offsetX | |
 ' |         |                                   |         | | screenHeight
 ' .         .                                   .         . .
 '
 ' Ora calcoliamo le dimensioni della finestra entro la quale disegneremo il 
 ' triangolo di Sierpinski (screenWidth x screenHeight pixels). Come regola 
 ' generale, utilizzeremo una finestra di 256 pixel di larghezza per una 
 ' altezza pari al massimo rappresentabile dall'hardware. Se vi sono meno di 
 ' 256 pixel disponibili, useremo quelli. Se vi sono più di 256 pixel 
 ' disponibili, il triangolo sarà centrato sullo schermo (con un offset 
 ' pari a offsetX pixel).
 '
 CONST screenWidth = IF(SCREEN WIDTH < 256, SCREEN WIDTH, 256)
 CONST screenHeight = SCREEN HEIGHT
 CONST offsetX = IF(SCREEN WIDTH < 256, 0, ( SCREEN WIDTH - screenWidth ) \ #2)
 
 ' The procedure for drawing the triangle requires three (starting) 
 ' coordinates, which are the vertices of the triangle to start from.
 '
 '                  * (x1,y1)
 '                 / \
 '                /   \
 '       (x2,y2) *-----* (x3,y3)
 '
 ' La procedura per disegnare il triangolo necessita di tre coordinate
 ' (di partenza), che sono i vertici del triangolo da cui partire. 
 '
 CONST x1=(screenWidth\#2): CONST y1=0
 CONST x2=0: CONST y2=(screenHeight-1)
 CONST x3=(screenWidth-1): CONST y3=(screenHeight-1)
 
 ' In order to ensure as "rectangular" distribution as possible of the points 
 ' chosen randomly, we generate an array of 256 elements. 
 ' This map is used as a "lookup table": at the input we have the random 
 ' number (which does have a irregular distribution) and at the 
 ' output we have a distribution of the abscissa of a rectangular type 
 ' (about 33% for each abscissa).
 '
 ' Thanks to Antonio Savona for the suggestion.
 '
 '  0 ...... 256
 ' +------------+         +------------+         +----+----+----+
 ' |  |  |      |         |            |         | x1 | x2 | x3 |
 ' | ||| ||| || | ======> |   xx(..)   | ======> +----+----+----+
 ' ||||||||| ||||         |            |         | 34%| 33%| 33%|
 ' +------------+         +------------+         +----+----+----+
 '
 ' Al fine di garantire una distribuzione il più possibile "rettangolare" 
 ' dei punti scelti casualmente, si è adottata la scelta di generare un 
 ' array di 256 elementi. Tale mappa viene utilizzata come una 
 ' "tabella di lookup": in ingresso abbiamo il numero casuale (che 
 ' non ha una distribuzione rettangolare) e in uscita abbiamo una 
 ' distribuzione delle ascisse di tipo rettangolare (circa 33% per 
 ' ogni ascissa).
 '
 ' Ringrazio Antonio Savona per il suggerimento.
 '
 DIM xx AS BYTE(256) = # { _
 		x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, _
 		x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, _
 		x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, _
 		x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, _
 		x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, _
 		x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, _
 		x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, _
 		x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, _
 		x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, _
 		x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, _
 		x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, _
 		x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, _
 		x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, _
 		x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, _
 		x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, _
 		x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1, x2, x3, x1  _
 	} READONLY
 
 ' See above / Si veda sopra.
 '
 DIM yy AS BYTE(256) = # { _
 		y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, _
 		y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, _
 		y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, _
 		y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, _
 		y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, _
 		y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, _
 		y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, _
 		y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, _
 		y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, _
 		y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, _
 		y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, _
 		y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, _
 		y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, _
 		y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, _
 		y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, _
 		y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1, y2, y3, y1  _
 	} READONLY
 
 ' We set the number of points to draw, at most. The challenge includes 10,000 points. 
 ' The greater the number of points, the more defined the triangles will be.
 ' We also calculate the value of a quarter of the points, as the algorithm will 
 ' draw four points at a time.
 '
 ' Impostiamo il numero di punti da disegnare, al massimo. La challenge prevede 10.000 
 ' punti. Maggiore è il numero di punti, più definiti saranno i triangoli.
 ' Calcoliamo anche il valore di un quarto dei punti, in quanto l'algoritmo disegnerà 
 ' quattro punti alla volta.
 '
 CONST limit = 10000
 
 ' We define the coordinates of each point as (x, y). These coordinates will be updated 
 ' as the triangle is drawn. The starting value coincides with the top vertex.
 '
 ' Definiamo le coordinate di ogni punto come (x, y). Tali coordinate saranno aggiornate 
 ' man mano che sarà disegnato il triangolo. Il valore iniziale coincide con il 
 ' vertice superiore.
 '
 x = #x1 AS POSITION
 y = #y1 AS POSITION
 
 ' This variable keeps the number of points drawn so far.
 '
 ' Questa variabile mantiene il numero di punti disegnati fino a questo momento.
 '
 n = #0 AS INTEGER
 
 ' Starting from this point we start the loop to draw the triangle. 
 ' It is a loop that will be repeated for the total number of points 
 ' to be drawn.
 '
 ' A partire da questo punto iniziamo il loop per disegnare il triangolo.
 ' Si tratta di un loop che sarà ripetuto per il numero di punti da 
 ' disegnare, complessivamente.
 '
 REPEAT
 
 	' We randomly choose one of the vertices from which to start to draw 
 	' the next point. As explained in the data flow diagram, the choice 
 	' starts from a number ranging from 0 to 255, the distribution of 
 	' which is not completely random.
 	'
 	' Scegliamo a caso uno dei vertici da cui partire per disegnare il 
 	' prossimo punto. Come spiegato nel diagramma di flusso dei dati, 
 	' la scelta parte da un numero che va da 0 a 255, la cui distribuzione 
 	' non è completamente causale. 
 	'
 	r = RANDOM BYTE
 
 	' If we were directly based on this number to decide which vertex to start 
 	' from, we would have vertices that would be chosen more frequently than 
 	' the others. This would result in a less defined image on the less 
 	' chosen points. To avoid this, we will use a large vector exactly like
 	' the number of random numbers that can be generated. This vector contains, 
 	' in an equidistributed way, the information on the acissa and the ordinate 
 	' of each vertex. Once chosen, this coefficient will be added to the current 
 	' coordinates, thus making the average. ugBASIC allows you to use syntax in 
 	' "prefix" form, ie where one of the operands is also the recipient of the 
 	' result of the operation. This is the meaning of the subsequent operations, 
 	' which update the coordinates to be drawn. 
 	'
 	' Se ci basassimo direttamente su questo numero per decidere da quale 
 	' vertice partire, avremmo dei vertici che sarebbero scelti con maggior 
 	' frequenza degli altri. Ciò determinerebbe una immagine meno definita sui 
 	' punti meno scelti. Per evitarlo, utilizzeremo un vettore grande esattamente 
 	' come il numero di numeri casuali generabili. Tale vettore contiene, in 
 	' modo equidistribuito, le informazioni sull'acissa e sull'ordinata di ogni vertice.
 	' Una volta scelto, tale coefficiente sarà aggiunto alle coordinate attuali, 
 	' facendone quindi la media. ugBASIC consente di utilizzare sintassi in forma 
 	' "prefissa", cioè dove uno degli operandi è anche il destinatario del risultato 
 	' dell'operazione. Questo è il significato delle operazioni successive, 
 	' che aggiornano le coodinate da disegnare.
 	'
 	' x = ( x + xx() ) / 2 
 	'       => x = x + xx(); x = x / 2
 	ADD x, xx(r) : DIV x, #2 
 	ADD y, yy(r) : DIV y, #2 
 
 	' Finally we can draw the point thus obtained.
 	'
 	' Finalmente possiamo disegnare il punto così ricavato.
 	'
 	PLOT offsetX + x, y
 
 	' Pass to next point.
 	'
 	' Passiamo al prossimo punto.
 	'
 	INC n
 
 ' We repeat the loop until we have drawn all the points.
 '
 ' Ripetiamo il loop fino a che non abbiamo disegnato tutti i punti.
 '
 UNTIL n = limit
 
 ' At the end we calculate how much time has passed, and show 
 ' it on the screen. Rounding is to the second.
 ' 
 ' Al termine calcoliamo quanto tempo è passato, e mostriamolo 
 ' a schermo. L'arrotondamento è al secondo.
 te = TI - t
 HOME
 PRINT "time = ";(te/TICKS PER SECOND);" sec"
 PRINT "points = ";limit

• contrib_sierpinski3.bas

The instructions here refer to compiling the example from the command line. For Microsoft Windows users we suggest using UGBASIC-IDE, which allows you to compile the example with just one click.

In order to compile and run the example, you need to have the Altirra emulator, and in particular that the altirra executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.atari contrib_sierpinski3.bas -o example.xex
 altirra example.xex
 
 # Windows 
 ugbc.atari.exe contrib_sierpinski3.bas -o example.xex
 altirra example.xex

In order to compile and run the example, you need to have the Altirra emulator, and in particular that the altirra executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.atarixl contrib_sierpinski3.bas -o example.xex
 altirra example.xex
 
 # Windows 
 ugbc.atarixl.exe contrib_sierpinski3.bas -o example.xex
 altirra example.xex

In order to compile and run the example, you need to have the VICE emulator, and in particular that the x64sc executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.c64 contrib_sierpinski3.bas -o example.prg
 x64sc example.prg
 
 # Windows 
 ugbc.c64.exe contrib_sierpinski3.bas -o example.prg
 x64sc example.prg

In order to run the example, you need to have the YAPE emulator. In particular that the yape executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.plus4 contrib_sierpinski3.bas -o example.prg
 yape example.prg
 
 # Windows 
 ugbc.plus4.exe contrib_sierpinski3.bas -o example.prg
 yape example.prg

In order to run the example, you need to have the VICE emulator. In particular that the xplus4 executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.plus4 contrib_sierpinski3.bas -o example.prg
 xplus4 example.prg
 
 # Windows 
 ugbc.plus4.exe contrib_sierpinski3.bas -o example.prg
 xplus4 example.prg

In order to compile and run the example, you need to have the XROAR emulator, and in particular that the xroar executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.d32 contrib_sierpinski3.bas -o example.bin
 xroar -rompath (your rom path) example.bin
 
 # Windows 
 ugbc.d32.exe contrib_sierpinski3.bas -o example.bin
 xroar.exe -rompath (your rom path) example.bin

In order to compile and run the example, you need to have the XROAR emulator, and in particular that the xroar executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.d64 contrib_sierpinski3.bas -o example.bin
 xroar -rompath (your rom path) example.bin
 
 # Windows 
 ugbc.d64.exe contrib_sierpinski3.bas -o example.bin
 xroar.exe -rompath (your rom path) example.bin

In order to compile and run the example, you need to have the DCMOTO emulator, and in particular that the dcmoto executable is accessible.

Then, type this command on the command line and on the emulator:

 # Linux 
 ugbc.pc128op contrib_sierpinski3.bas -o example.k7
 dcmoto
 (choose BASIC 128)
 CLEAR,&H2FFF: LOADM"CASS:",R: EXEC
 
 # Windows 
 ugbc.pc128op.exe contrib_sierpinski3.bas -o example.k7
 dcmoto
 (choose example.k7)
 (choose BASIC 128)
 CLEAR,&H2FFF: LOADM"CASS:",R: EXEC

In order to compile and run the example, you need to have the DCMOTO emulator, and in particular that the dcmoto executable is accessible.

Then, type this command on the command line and on the emulator:

 # Linux 
 ugbc.pc128op contrib_sierpinski3.bas -o example.k7
 dcmoto
 (choose BASIC 128)
 CLEAR,&H2FFF: LOADM"CASS:",R: EXEC
 
 # Windows 
 ugbc.pc128op.exe contrib_sierpinski3.bas -o example.k7
 dcmoto
 (choose example.k7)
 (choose BASIC 128)
 CLEAR,&H2FFF: LOADM"CASS:",R: EXEC

In order to compile and run the example, you need to have the VICE emulator, and in particular that the xvic executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.vic20 contrib_sierpinski3.bas -o example.prg
 xvic --memory 24k example.prg
 
 # Windows 
 ugbc.vic20.exe contrib_sierpinski3.bas -o example.prg
 xvic --memory 24k example.prg

In order to compile and run the example, you need to have the Speccy emulator, and in particular that the speccy executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.zx contrib_sierpinski3.bas -o example.tap
 Speccy example.tap
 
 # Windows 
 ugbc.zx.exe contrib_sierpinski3.bas -o example.tap
 Speccy example.tap

In order to compile and run the example, you need to have the openMsx or the BlueMSX emulator, and in particular that its executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.msx1 contrib_sierpinski3.bas -o example.rom
 openmsx -cart example.rom
 
 # Windows 
 ugbc.msx1.exe contrib_sierpinski3.bas -o example.rom
 openmsx -cart example.rom

 # Linux 
 ugbc.msx1 contrib_sierpinski3.bas -o example.rom
 bluemsx example.rom
 
 # Windows 
 ugbc.msx1.exe contrib_sierpinski3.bas -o example.rom
 bluemsx example.rom

In order to compile and run the example, you need to have the openMsx or the BlueMSX emulator, and in particular that its executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.coleco contrib_sierpinski3.bas -o example.rom
 openmsx -machine \"COL - ColecoVision\" -cart example.rom
 
 # Windows 
 ugbc.coleco.exe contrib_sierpinski3.bas -o example.rom
 bluemsx -machine \"COL - ColecoVision\" example.rom

 # Linux 
 ugbc.coleco contrib_sierpinski3.bas -o example.rom
 bluemsx /machine \"COL - ColecoVision\" /rom1 example.rom
 
 # Windows 
 ugbc.coleco.exe contrib_sierpinski3.bas -o example.rom
 bluemsx  /machine \"COL - ColecoVision\" /rom1 example.rom

In order to compile and run the example, you need to have the BlueMSX emulator, and in particular that its executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.sc3000 contrib_sierpinski3.bas -o example.rom
 bluemsx /machine \"SEGA - SC-3000\" /rom1 example.rom
 
 # Windows 
 ugbc.sc3000.exe contrib_sierpinski3.bas -o example.rom
 bluemsx  /machine \"SEGA - SC-3000\" /rom1 example.rom

In order to compile and run the example, you need to have the BlueMSX emulator, and in particular that its executable is accessible.

Then, type this command on the command line:

 # Linux 
 ugbc.sg1000 contrib_sierpinski3.bas -o example.rom
 bluemsx /machine \"SEGA - SG-1000\" /rom1 example.rom
 
 # Windows 
 ugbc.sg1000.exe contrib_sierpinski3.bas -o example.rom
 bluemsx  /machine \"SEGA - SG-1000\" /rom1 example.rom

If you have found a problem trying to run this example, if you think there is a bug or, more simply, you would like it to be improved, open an issue for this example on GitHub. Thank you!