Kits
›
La máquina de fractales
RU
EN
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Contenido
Introduction
History: patterns that repeat themselves
Lesson 0. Gates from transistors: for those who start from scratch
0.1. The idea: a transistor is a switch
0.2. Building
0.3. Check
Lesson 0 paste (Cmd+I)
Lesson 1. Memory: the latch and the D flip-flop
1.1. The idea: a loop that holds
1.2. Building
1.3. Check
Lesson 1 paste (Cmd+I)
Lesson 2. The counter: six flip-flops count to 63
2.1. The idea: add 1 in a column
2.2. Building
2.3. Check
Lesson 2 paste (Cmd+I)
Lesson 3. The raster scan: the screen dot by dot
3.1. The idea: the beam runs along the rows
3.2. Building
Try the patterns
3.3. Check
Lesson 3 paste (Cmd+I)
Lesson 4. The Sierpinski triangle: a fractal from ten gates
4.1. The idea: not a single common bit
4.2. Building
4.3. Check
Lesson 4 paste (Cmd+I)
Lesson 5. The chaos game: a triangle from chance
5.1. The idea: a half-way step
5.2. The idea: a step is a shift
5.3. Building
5.4. Check
Lesson 5 paste (Cmd+I)
Lesson 6 (bonus). Munching Squares: a living pattern from 1962
6.1. The idea: (x XOR y) < t
6.2. Building
6.3. Check
Lesson 6 paste (Cmd+I)
Summary
All the parts
Instructions in pictures
Lesson 5 in pictures
← Back to the lesson: Lesson 5. The chaos game: a triangle from chance
5
The chaos game
the same triangle from random dots
kh
HB-03
IN
5×
OUT
8×
NOT
4×
0
XOR
3×
0
AND
20×
0
OR
3×
0
DFF
18×
1
1×
∞
Ctrl
+
G
LFSR12
SHIFT6
© 2026 Daniil Khanin · khanin.info · HB-03
30
LFSR12
1
IN
2×
OUT
2×
NOT
1×
0
XOR
2×
0
8×
CLK
RST
A
B
NOT
I0
RST
O0
nRST
XOR
I0
r11
I1
r5
O0
f1
XOR
I0
f1
I1
r3
O0
f2
2
XOR
1×
0
AND
1×
0
OR
1×
0
9×
XOR
I0
f2
I1
r0
O0
fb
AND
I0
fb
I1
nRST
O0
g0
OR
I0
g0
I1
RST
O0
d0
© 2026 Daniil Khanin · khanin.info · HB-03
31
LFSR12 …
3
DFF
2×
1
AND
1×
0
9×
DFF
D
d0
CLK
CLK
Q
r0
nQ
AND
I0
r0
I1
nRST
O0
d1
DFF
D
d1
CLK
CLK
Q
r1
nQ
4
AND
2×
0
DFF
1×
1
9×
AND
I0
r1
I1
nRST
O0
d2
DFF
D
d2
CLK
CLK
Q
r2
nQ
AND
I0
r2
I1
nRST
O0
d3
© 2026 Daniil Khanin · khanin.info · HB-03
32
LFSR12 …
5
DFF
2×
1
AND
1×
0
9×
DFF
D
d3
CLK
CLK
Q
r3
nQ
AND
I0
r3
I1
nRST
O0
d4
DFF
D
d4
CLK
CLK
Q
r4
nQ
6
AND
2×
0
DFF
1×
1
9×
AND
I0
r4
I1
nRST
O0
d5
DFF
D
d5
CLK
CLK
Q
r5
nQ
AND
I0
r5
I1
nRST
O0
d6
7
DFF
2×
1
AND
1×
0
9×
DFF
D
d6
CLK
CLK
Q
r6
nQ
AND
I0
r6
I1
nRST
O0
d7
DFF
D
d7
CLK
CLK
Q
r7
nQ
© 2026 Daniil Khanin · khanin.info · HB-03
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LFSR12 …
8
AND
2×
0
DFF
1×
1
9×
AND
I0
r7
I1
nRST
O0
d8
DFF
D
d8
CLK
CLK
Q
r8
nQ
AND
I0
r8
I1
nRST
O0
d9
9
DFF
2×
1
AND
1×
0
9×
DFF
D
d9
CLK
CLK
Q
r9
nQ
AND
I0
r9
I1
nRST
O0
d10
DFF
D
d10
CLK
CLK
Q
r10
nQ
10
AND
1×
0
DFF
1×
1
OR
1×
0
9×
AND
I0
r10
I1
nRST
O0
d11
DFF
D
d11
CLK
CLK
Q
r11
nQ
OR
I0
r0
I1
r0
O0
A
© 2026 Daniil Khanin · khanin.info · HB-03
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LFSR12 …
SHIFT6
11
OR
1×
0
3×
OR
I0
r6
I1
r6
O0
B
12
Ctrl
+
G
Library
…
Chip N
2×
Library
…
LFSR12
Enter
LFSR12
CLK
RST
A
B
13
IN
3×
OUT
6×
CLK
RST
IN
Q0
Q1
Q2
Q3
Q4
Q5
14
NOT
1×
0
AND
1×
0
DFF
1×
1
8×
NOT
I0
RST
O0
nRST
AND
I0
IN
I1
nRST
O0
d5
DFF
D
d5
CLK
CLK
Q
Q5
nQ
© 2026 Daniil Khanin · khanin.info · HB-03
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SHIFT6 …
15
AND
2×
0
DFF
1×
1
9×
AND
I0
Q5
I1
nRST
O0
d4
DFF
D
d4
CLK
CLK
Q
Q4
nQ
AND
I0
Q4
I1
nRST
O0
d3
16
DFF
2×
1
AND
1×
0
9×
DFF
D
d3
CLK
CLK
Q
Q3
nQ
AND
I0
Q3
I1
nRST
O0
d2
DFF
D
d2
CLK
CLK
Q
Q2
nQ
17
AND
2×
0
DFF
1×
1
9×
AND
I0
Q2
I1
nRST
O0
d1
DFF
D
d1
CLK
CLK
Q
Q1
nQ
AND
I0
Q1
I1
nRST
O0
d0
© 2026 Daniil Khanin · khanin.info · HB-03
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SHIFT6 …
CANVAS
18
DFF
1×
1
3×
DFF
D
d0
CLK
CLK
Q
Q0
nQ
19
Ctrl
+
G
Library
…
Chip N
2×
Library
…
SHIFT6
Enter
SHIFT6
CLK
RST
IN
Q0
Q1
Q2
Q3
Q4
Q5
20
Dot display → ⚙: Layout Dots, 64 × 64, Port width 1 dot
21
LFSR12
1×
NOT
2×
0
8×
LFSR12
CLK
CLK
RST
RST
A
ra
B
rb
NOT
I0
ra
O0
nra
NOT
I0
rb
O0
nrb
© 2026 Daniil Khanin · khanin.info · HB-03
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CANVAS …
22
AND
2×
0
6×
AND
I0
ra
I1
nrb
O0
kx
AND
I0
rb
I1
nra
O0
ky
23
SHIFT6
1×
9×
SHIFT6
CLK
CLK
RST
RST
IN
kx
Q0
px0
Q1
px1
Q2
px2
Q3
px3
Q4
px4
Q5
px5
24
SHIFT6
1×
9×
SHIFT6
CLK
CLK
RST
RST
IN
ky
Q0
py0
Q1
py1
Q2
py2
Q3
py3
Q4
py4
Q5
py5
© 2026 Daniil Khanin · khanin.info · HB-03
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CANVAS …
25
1×
16×
Dot display
X0
px0
X1
px1
X2
px2
X3
px3
X4
px4
X5
px5
Y0
py0
Y1
py1
Y2
py2
Y3
py3
Y4
py4
Y5
py5
D0
VCC
WE
VCC
CLK
nCLK
CLR
GND
© 2026 Daniil Khanin · khanin.info · HB-03
39
← Back to the lesson
Lesson 5. The chaos game: a triangle from chance