Hothouse Plot

This program draws a polar rose curve on screen using the parametric equations X = R·cos(T) and Y = R·sin(T), where R = P·sin(N·T). With N set to 456 and P to 20, it produces a dense multi-petalled flower pattern centred at coordinate (31, 21). The program pre-computes 601 data points into DIM arrays during FAST mode, then switches to SLOW mode for plotting, separating calculation from display for efficiency. After a short delay loop (lines 100–110), it loops back to clear the screen and redraw continuously, creating an animated cycling effect.

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Program Analysis

Program Structure

The program is divided into four logical phases:

1. Initialisation (lines 5–40): Sets the petal count N=456, angular step D=2*PI/600, and amplitude P=20; allocates two 601-element arrays.
2. Computation in FAST mode (lines 40–72): Iterates I from 0 to 600, computing polar coordinates and converting them to Cartesian X/Y values stored in the arrays.
3. Display in SLOW mode (lines 74–90): Clears the screen and plots all 601 pre-computed points.
4. Loop and repeat (lines 100–130): A 100-iteration delay loop followed by GOTO 76 continuously redraws the same curve, creating an animation cycle.

Mathematical Technique

The curve is a polar rose defined by R = P * SIN(N * T), where T ranges from 0 to 2π in 600 equal steps. This is converted to screen coordinates via:

• X(I+1) = R * COS(T) + 31 — centred horizontally at column 31
• Y(I+1) = R * SIN(T) + 21 — centred vertically at row 21

With N=456 (an even integer), the rose produces 2×456 = 912 petals in theory, though the limited 64×44 pixel ZX81 display resolution means many petals overlap or fall outside the visible area. The amplitude P=20 keeps the curve within the screen bounds.

FAST/SLOW Mode Usage

The program explicitly uses FAST (line 6) during the computationally intensive array-filling loop and switches to SLOW (line 74) only for the display phase. This is a standard ZX81 optimisation: FAST suppresses the display interrupt, allowing the CPU to run at full speed for floating-point calculations, while SLOW re-enables the display driver for visible output.

Array Pre-computation Strategy

Rather than computing and plotting each point in a single pass, all 601 X and Y values are stored in DIM X(601) and DIM Y(601) before any plotting occurs. This costs RAM (each array element occupies 5 bytes in ZX81 floating-point format, so ~6 KB total for both arrays) but cleanly separates the FAST computation phase from the SLOW display phase.

Delay and Animation Loop

Lines 100–110 implement a busy-wait delay via an empty FOR/NEXT loop of 100 iterations. After the delay, GOTO 76 jumps back to the CLS at line 76 rather than line 5, so the arrays are never recomputed — only the screen is cleared and the curve redrawn from the cached data.

Key Variables

Variable	Purpose
N	Petal frequency parameter (456)
D	Angular increment (2π/600)
P	Amplitude / petal length (20)
T	Current angle in radians
R	Current polar radius
X(), Y()	Pre-computed Cartesian coordinates
I	Loop counter (dual use: fill and plot)

Notable Anomalies

Line 130 (CLEAR) and lines 140–150 (SAVE / RUN) are never reached during normal execution because GOTO 76 at line 120 creates an infinite loop. These lines serve as a save-and-autostart block appended after the main program logic.