This example is the optimized 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
 ' ============================================================================
 
 ' We start measure time from the graphical initialization.
 t=TI
 
 ' Enable the monocrome bitmap graphic, 
 ' with a minimum resolution of 160x100 pixels.
 BITMAP ENABLE(320,200,2)
 
 ' Pen color is black
 INK BLACK
 
 ' Paper color is white
 CLS WHITE
 
 ' Let's calculate the three constants
 CONST x1=(SCREEN WIDTH \ #2): CONST y1=0
 CONST x2=0: CONST y2=(SCREEN HEIGHT - 1 )
 CONST x3=(SCREEN WIDTH - 1): CONST y3=(SCREEN HEIGHT - 1 )
 
 ' Number of points to draw
 CONST limit = 10000
 
 ' ============================================================================
 ' MAIN CYCLE
 ' ============================================================================
 
 ' Initialize the coordinates.
 x=#x1 AS POSITION
 y=#y1 AS POSITION
 
 ' Initialize the counter.
 n=#0 AS INTEGER
 
 ' Repeat the cycle up to (limit) points.
 REPEAT
 
 	' Select a random triangle
 	r=(RANDOM BYTE \ 32) AND 3
 	
 	' If the triange has been chosen...
 	IF r=0 THEN 
 		' Update the coordinates accordingly.
 		ADD x, x1 : DIV x, #2 
 		ADD y, y1 : DIV y, #2 
 	ELSE IF r=1 THEN 
 		ADD x, x2 : DIV x, #2
 		ADD y, y2 : DIV y, #2
 	ELSE
 		ADD x, x3 : DIV x, #2
 		ADD y, y3 : DIV y, #2
 	ENDIF
 	
 	' Plot the point on the screen.
 	PLOT x, y
 
 	' Increment the number of point traced.
 	INC n
 
 UNTIL n=limit
 
 ' Calculate the time passed
 te=TI-t
 
 HOME
 ' Print the stats
 PRINT "time = ";(te/TICKS PER SECOND);" sec"
 PRINT "points = ";n%
 

• contrib_sierpinski2.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_sierpinski2.bas -o example.xex
 altirra example.xex
 
 # Windows 
 ugbc.atari.exe contrib_sierpinski2.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_sierpinski2.bas -o example.xex
 altirra example.xex
 
 # Windows 
 ugbc.atarixl.exe contrib_sierpinski2.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_sierpinski2.bas -o example.prg
 x64sc example.prg
 
 # Windows 
 ugbc.c64.exe contrib_sierpinski2.bas -o example.prg
 x64sc example.prg

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.c64reu contrib_sierpinski2.bas -o example.prg
 x64sc -reu example.prg
 
 # Windows 
 ugbc.c64reu.exe contrib_sierpinski2.bas -o example.prg
 x64sc -reu 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_sierpinski2.bas -o example.prg
 yape example.prg
 
 # Windows 
 ugbc.plus4.exe contrib_sierpinski2.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_sierpinski2.bas -o example.prg
 xplus4 example.prg
 
 # Windows 
 ugbc.plus4.exe contrib_sierpinski2.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_sierpinski2.bas -o example.bin
 xroar -rompath (your rom path) example.bin
 
 # Windows 
 ugbc.d32.exe contrib_sierpinski2.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_sierpinski2.bas -o example.bin
 xroar -rompath (your rom path) example.bin
 
 # Windows 
 ugbc.d64.exe contrib_sierpinski2.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_sierpinski2.bas -o example.k7
 dcmoto
 (choose BASIC 128)
 CLEAR,&H2FFF: LOADM"CASS:",R: EXEC
 
 # Windows 
 ugbc.pc128op.exe contrib_sierpinski2.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_sierpinski2.bas -o example.k7
 dcmoto
 (choose BASIC 128)
 CLEAR,&H2FFF: LOADM"CASS:",R: EXEC
 
 # Windows 
 ugbc.pc128op.exe contrib_sierpinski2.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_sierpinski2.bas -o example.prg
 xvic --memory 24k example.prg
 
 # Windows 
 ugbc.vic20.exe contrib_sierpinski2.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_sierpinski2.bas -o example.tap
 Speccy example.tap
 
 # Windows 
 ugbc.zx.exe contrib_sierpinski2.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_sierpinski2.bas -o example.rom
 openmsx -cart example.rom
 
 # Windows 
 ugbc.msx1.exe contrib_sierpinski2.bas -o example.rom
 openmsx -cart example.rom

 # Linux 
 ugbc.msx1 contrib_sierpinski2.bas -o example.rom
 bluemsx example.rom
 
 # Windows 
 ugbc.msx1.exe contrib_sierpinski2.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_sierpinski2.bas -o example.rom
 openmsx -machine \"COL - ColecoVision\" -cart example.rom
 
 # Windows 
 ugbc.coleco.exe contrib_sierpinski2.bas -o example.rom
 bluemsx -machine \"COL - ColecoVision\" example.rom

 # Linux 
 ugbc.coleco contrib_sierpinski2.bas -o example.rom
 bluemsx /machine \"COL - ColecoVision\" /rom1 example.rom
 
 # Windows 
 ugbc.coleco.exe contrib_sierpinski2.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_sierpinski2.bas -o example.rom
 bluemsx /machine \"SEGA - SC-3000\" /rom1 example.rom
 
 # Windows 
 ugbc.sc3000.exe contrib_sierpinski2.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_sierpinski2.bas -o example.rom
 bluemsx /machine \"SEGA - SG-1000\" /rom1 example.rom
 
 # Windows 
 ugbc.sg1000.exe contrib_sierpinski2.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!