---
title: "Hothouse Plot"
id: 56805
type: "computer_media"
slug: "hothouse-plot"
url: "http://localhost/computer_media/hothouse-plot/"
markdown_url: "http://localhost/computer_media/hothouse-plot.md"
published_at: "2024-09-29T02:04:07+00:00"
modified_at: "2026-03-30T21:21:01+00:00"
author: "David Anderson"
featured_image:
  url: "http://localhost/wp-content/uploads/2024/09/297_HP.png"
excerpt: "A mesmerising polar rose with 456 petals is pre-calculated into arrays and continuously redrawn — see how parametric maths produces intricate floral geometry."
category:
  - name: "Archived Media"
    slug: "archived-media"
    taxonomy: "category"
    url: "http://localhost/category/archived-media/"
post_tag:
  - name: "Downloadable"
    slug: "downloadable"
    taxonomy: "post_tag"
    url: "http://localhost/tag/downloadable/"
  - name: "TS 1000"
    slug: "ts1000"
    taxonomy: "post_tag"
    url: "http://localhost/tag/ts1000/"
model:
  - name: "Timex/Sinclair 1000"
    slug: "ts-1000"
    taxonomy: "model"
    url: "http://localhost/model/ts-1000/"
genre:
  - name: "Demo"
    slug: "demo"
    taxonomy: "genre"
    url: "http://localhost/type/demo/"
media_contents:
  - id: 56738
    title: "Timex Sinclair Public Domain Library Tape 1007"
    type: "computer_media"
    url: "http://localhost/computer_media/timex-sinclair-public-domain-library-tape-1007/"
media_type: "Program"
mediadate: "198x"
images:
  - url: "http://localhost/wp-content/uploads/2024/09/297_HP.png"
media_type_tags: "Demo"
---

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.

***

## 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.

## Source Code

```
   5 REM HOTHOUSE PLOT
   6 FAST 
   7 DIM X(601)
   8 DIM Y(601)
  10 LET N=456
  20 LET D=2*PI/600
  30 LET P=20
  40 FOR I=0 TO 600
  50 LET T=D*I
  55 LET R=P*SIN (N*T)
  60 LET X(I+1)=R*COS T+31
  70 LET Y(I+1)=R*SIN T+21
  72 NEXT I
  74 SLOW 
  76 CLS 
  78 FOR I=1 TO 601
  80 PLOT X(I),Y(I)
  90 NEXT I
 100 FOR I=1 TO 100
 110 NEXT I
 120 GOTO 76
 130 CLEAR 
 140 SAVE "1029%7"
 150 RUN
```