Lesson 1. The 128 × 128 screen: seven bits instead of six

After this lesson the Sierpinski triangle draws itself on a 128 × 128 screen — the same one as in The Fractal Machine, but four times as detailed. This is a test of the new screen and the scan: in lesson 5 the Mandelbrot set is computed on the same kind of scan.

1.1. The idea: one more bit

The dot number along each axis is a binary number. A 64 × 64 screen needed 6 bits, and 128 = 2⁷ needs a seventh. Everything else is the same scan:

• counter X runs along the row, the next dot on every clock;
• at the end of the row its carry cx moves the row counter Y;
• a frame is 128 × 128 = 16,384 clocks.

1.2. The idea: reset from outside

In The Fractal Machine every counter inverted RST with its own NOT. Real circuits do it differently: the reset arrives already inverted — nRST, "0 means reset" — and there is one NOT for the whole board. In this kit we do the same: counters, registers and the random generator get nRST. The screen is cleared by RST itself, on its CLR pin.

1.3. Building

New project. You need the chips NOT, XOR, AND, OR, NOR, DFF from HB-03. Place Power and Ground.

Step 1. CNT7 — a seven-bit counter

Ctrl+G → name CNT7. Pins: inputs CLK, EN, nRST; outputs Q0–Q6, CO.

Step 2. The screen

Place a Dot display and set it up in ⚙:

Step 3. Canvas: clock, reset, two counters, the Sierpinski pattern, the screen

The test pattern is the Sierpinski triangle from HB-03, now on seven bits: a dot is lit if (x AND y) = 0.

The Clock at 60Hz shows the scan running, but a frame of 16,384 dots takes 4.5 minutes. Click the clock body up to 4kHz — a frame in 4 seconds.

1.4. Check

If only the top half of the screen is lit, check the Dot display pin Y6 (label y6) and Height, dots = 128. If the picture repeats, the seventh bit of one of the CNT7 is not on its label.

Lesson 1 paste (Cmd+I)

You need NOT, XOR, AND, OR, NOR, DFF from The Fractal Machine (lessons 0 and 1).

# Lesson 1 — the 128 x 128 screen: the 7-bit counter CNT7 and the raster scan; check — the Sierpinski triangle.chip CNT7 {  portIn(CLK)  portIn(EN)  portIn(nRST)  portOut(Q0)  portOut(Q1)  portOut(Q2)  portOut(Q3)  portOut(Q4)  portOut(Q5)  portOut(Q6)  portOut(CO)  XOR(Q0, EN, t0)  AND(t0, nRST, d0)  AND(EN, Q0, c1)  DFF(D=d0, CLK=CLK, Q=Q0)  XOR(Q1, c1, t1)  AND(t1, nRST, d1)  AND(c1, Q1, c2)  DFF(D=d1, CLK=CLK, Q=Q1)  XOR(Q2, c2, t2)  AND(t2, nRST, d2)  AND(c2, Q2, c3)  DFF(D=d2, CLK=CLK, Q=Q2)  XOR(Q3, c3, t3)  AND(t3, nRST, d3)  AND(c3, Q3, c4)  DFF(D=d3, CLK=CLK, Q=Q3)  XOR(Q4, c4, t4)  AND(t4, nRST, d4)  AND(c4, Q4, c5)  DFF(D=d4, CLK=CLK, Q=Q4)  XOR(Q5, c5, t5)  AND(t5, nRST, d5)  AND(c5, Q5, c6)  DFF(D=d5, CLK=CLK, Q=Q5)  XOR(Q6, c6, t6)  AND(t6, nRST, d6)  AND(c6, Q6, CO)  DFF(D=d6, CLK=CLK, Q=Q6)} clock{rt=60}(CLK)input(RST)NOT(RST, nRST)NOT(CLK, nCLK)CNT7(CLK=CLK, EN=VCC, nRST=nRST, Q0=x0, Q1=x1, Q2=x2, Q3=x3, Q4=x4, Q5=x5, Q6=x6, CO=cx)CNT7(CLK=CLK, EN=cx, nRST=nRST, Q0=y0, Q1=y1, Q2=y2, Q3=y3, Q4=y4, Q5=y5, Q6=y6, CO=cy)AND(x0, y0, a0)AND(x1, y1, a1)AND(x2, y2, a2)AND(x3, y3, a3)AND(x4, y4, a4)AND(x5, y5, a5)AND(x6, y6, a6)OR(a0, a1, o01)OR(a2, a3, o23)OR(a4, a5, o45)OR(o01, o23, o03)OR(o45, a6, o46)NOR(o03, o46, pix)dotdisplay SCR{layout=dots, w=128, h=128}(X0=x0, X1=x1, X2=x2, X3=x3, X4=x4, X5=x5, X6=x6, Y0=y0, Y1=y1, Y2=y2, Y3=y3, Y4=y4, Y5=y5, Y6=y6, D0=pix, WE=VCC, CLK=nCLK, CLR=RST)